JEE MAIN Complex Number Previous Year Question Paper and Solution with PDF

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Complex Number PYQ

Qus : 1 JEE MAIN PYQ

The region represented by {z = x + iy $ \in $ C : |z| – Re(z) $ \le $ 1} is also given by the inequality :{z = x + iy $ \in $ C : |z| – Re(z) $ \le $ 1}

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Morning) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\overline{z})^2 + |z| = 0,\; z \in \mathbb{C}$. Then $4(\alpha^2 + \beta^2)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $z = \left(\dfrac{\sqrt{3}}{2} + \dfrac{i}{2}\right)^5 + \left(\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right)^5.$ If $R(z)$ and $I(z)$ respectively denote the real and imaginary parts of $z$, then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

If $z = x+iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5i|=0$, then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

The number of complex numbers $z$ satisfying $|z|=1$ and $\left|\dfrac{z}{\overline{z}}+\dfrac{\overline{z}}{z}\right|=1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

Let C be the set of all complex numbers. Let ${S_1} = \{ z \in C||z - 3 - 2i{|^2} = 8\} $ ${S_2} = \{ z \in C|{\mathop{\rm Re}\nolimits} (z) \ge 5\} $ and ${S_3} = \{ z \in C||z - \overline z | \ge 8\} $. Then the number of elements in ${S_1} \cap {S_2} \cap {S_3}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 July Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

Let z $ \in $ C with Im(z) = 10 and it satisfies ${{2z - n} \over {2z + n}}$ = 2i - 1 for some natural number n. Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let the product of $\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta$ and $\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta$ be $\alpha+i\beta$, where $i=\sqrt{-1}$. Let $p$ and $q$ be the maximum and the minimum values of $\alpha+\beta$ respectively. Then $p+q$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $a,b$ be two real numbers such that $ab<0$. If the complex number $\dfrac{1+ai}{\,b+i\,}$ is of unit modulus and $a+ib$ lies on the circle $|z-1|=|2z|$, then a possible value of $\dfrac{1+[a]}{4b}$, where $[\,\cdot\,]$ is the greatest integer function, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

If $z$ is a complex number such that $|z|\ge 2$, then the minimum value of $\left|z+\dfrac{1}{2}\right|$ :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 11 JEE MAIN PYQ

Let z = x + iy be a non-zero complex numbersuch that ${z^2} = i{\left| z \right|^2}$, where i = $\sqrt { - 1} $ , then z lieson the :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Evening) PYQ

Solution

Qus : 12 JEE MAIN PYQ

The area (in sq. units) of the region $S = \{\, z \in \mathbb{C} : |z - 1| \le 2,\ (z + \bar{z}) + i(z - \bar{z}) \le 2,\ \operatorname{Im}(z) \ge 0 \,\}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

$ \text{Let } f,g : \mathbb{N} - \{1\} \to \mathbb{N} \text{ be functions defined by } f(a) = \alpha, \text{ where } \alpha \text{ is the maximum of the powers of those primes } p \text{ such that } p^\alpha \text{ divides } a, \text{ and } g(a) = a+1, \text{ for all } a \in \mathbb{N} - \{1\}. \text{ Then, the function } f+g \text{ is} $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Morning Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Consider the following two statements: Statement I: For any two non-zero complex numbers $z_1,z_2$, $(|z_1|+|z_2|)\left|\dfrac{z_1}{|z_1|}+\dfrac{z_2}{|z_2|}\right|\le 2(|z_1|+|z_2|)$. Statement II: If $x,y,z$ are three distinct complex numbers and $a,b,c$ are positive real numbers such that $\dfrac{a}{|,y-z,|}=\dfrac{b}{|,z-x,|}=\dfrac{c}{|,x-y,|}$, then $\dfrac{a^{2}}{,y-z,}+\dfrac{b^{2}}{,z-x,}+\dfrac{c^{2}}{,x-y,}=1$. Between the above two statements:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for all $z \in \mathbb{C}$ satisfying $|z| = 1$ and $\operatorname{Re} z \ne 1$, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

If $S = \{ z \in \mathbb{C} : |z - i| = |z + i| = |z - 1| \}$, then $n(S)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Among the statements (S1): The set ${z\in\mathbb{C}\setminus{-i}:\ |z|=1\ \text{ and }\ \dfrac{z-i}{z+i}\ \text{is purely real}}$ contains exactly two elements and (S2): The set ${z\in\mathbb{C}\setminus{-1}:\ |z|=1\ \text{ and }\ \dfrac{z-1}{z+1}\ \text{is purely imaginary}}$ contains infinitely many elements.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let $A = \{ z \in C:1 \le |z - (1 + i)| \le 2\} $

and $B = \{ z \in A:|z - (1 - i)| = 1\} $. Then, B :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+z^2}\right)$ equals :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

Qus : 20 JEE MAIN PYQ

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x - 2i = 0$, where $i = \sqrt{-1}$, then $16 \cdot \text{Re}\left( \dfrac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^5 + \beta^5} \right) \cdot \text{Im}\left( \dfrac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^5 + \beta^5} \right)$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Morning Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

Let $a\ne b$ be two non-zero real numbers. Then the number of elements in the set $X=\{\, z\in\mathbb{C} : \operatorname{Re}(a z^{2}+bz)=a \text{ and } \operatorname{Re}(b z^{2}+a z)=b \,\}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (6 April Evening Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

Among the statements: (S1): $2023^{2022}-1999^{2022}$ is divisible by $8$. (S2): $13(13)^n-12n-13$ is divisible by $144$ for infinitely many $n\in\mathbb{N}$.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (6 April Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

Let $\left(-2-\dfrac{1}{3}i\right)^{3}=e^{\frac{x+iy}{2\pi i}}\ (i=\sqrt{-1})$, where $x$ and $y$ are real numbers, then $\,y-x\,$ equals :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Morning Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

The equation $\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$ represents a circle with :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Morning Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

If $|z - 3 + 2i| \le 4$ then the difference between the greatest value and the least value of $|z|$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

If the locus of $z\in\mathbb{C}$, such that $\operatorname{Re}!\left(\dfrac{z-1}{2z+i}\right)+\operatorname{Re}!\left(\dfrac{z-1}{2z-i}\right)=2$, is a circle of radius $r$ and center $(a,b)$, then $\dfrac{15ab}{r^2}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Evening Shift) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let $S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}$ and $S_3=\{z \in \mathbf{C}: \operatorname{Re}(z) \geq 0\}$. Then the area of the region $S_1 \cap S_2 \cap S_3$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

Let $S_{1} = \{ z_{1} \in \mathbb{C} : |z_{1} - 3| = \tfrac{1}{2} \}$ and $S_{2} = \{ z_{2} \in \mathbb{C} : |z_{2} - |z_{2} + 1|| = |z_{2} + |z_{2} - 1|| \}$. Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$, the least value of $|z_{2} - z_{1}|$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

Let $z$ be a complex number such that $|z|+z=3+i$ (where $i=\sqrt{-1}$). Then $|z|$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

If ${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$, then p and q are roots of the equation :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

If $\alpha$, $\beta$ $\in$ R are such that 1 $-$ 2i (here i² = $-$1) is a root of z² + $\alpha$z + $\beta$ = 0, then ($\alpha$ $-$ $\beta$) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 February Evening Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

Let $A=\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1-i \sin \theta}\right.$ is purely imaginary $\}$. Then the sum of the elements in $\mathrm{A}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Evening Shift) PYQ

Solution

Qus : 34 JEE MAIN PYQ

$S = { z \in \mathbb{C} : \dfrac{z - i}{z + 2i} \in \mathbb R }$, then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 August Morning Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

If $\alpha, \beta \in \mathbb{C}$ are the distinct roots of the equation $x^{2} - x + 1 = 0$, then $\alpha^{101} + \beta^{107}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 36 JEE MAIN PYQ

If $\displaystyle \frac{z-\alpha}{z+\alpha}\ (\alpha\in\mathbb{R})$ is a purely imaginary number and $|z|=2$, then a value of $\alpha$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Morning Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

If $z = 2 + 3i$, then $z^5 + (\bar{z})^5$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

Let a circle C in complex plane pass through the points ${z_1} = 3 + 4i$, ${z_2} = 4 + 3i$ and ${z_3} = 5i$. If $z( \ne {z_1})$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then $arg(z)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Morning Shift) PYQ

Solution

Qus : 39 JEE MAIN PYQ

Let z₁ and z₂ be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi $. Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

If $z=\dfrac{1}{2}-2i$ is such that $|z+1|=\alpha z+\beta(1+i)$, $i=\sqrt{-1}$ and $\alpha,\beta\in\mathbb{R}$, then $\alpha+\beta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

Let $O$ be the origin, the point $A$ be $z_1=\sqrt{3}+2\sqrt{2},i$, the point $B$ $(z_2)$ be such that $\sqrt{3},|z_2|=|z_1|$ and $\arg(z_2)=\arg(z_1)+\dfrac{\pi}{6}$. Then

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

If $z \neq 0$ be a complex number such that $\left|z - \frac{1}{z}\right| = 2$, then the maximum value of $|z|$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Evening Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

The complex number $z=x+iy$ is such that $\dfrac{2z-3i}{2z+i}$ is purely imaginary. If $x+y^{2}=0$, then $y^{4}+y^{2}-y$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Morning Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

The set $S = \{ z = x + i y : \dfrac{2z - 3i}{4z + 2i} \text{ is a real number} \}$ is given. Then which of the following is **NOT correct**?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Evening Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

Let $A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$ and $B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}$. Then A $\cap$ B is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Morning Shift) PYQ

Solution

Qus : 46 JEE MAIN PYQ

If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$, then

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

The least positive integer $n$ for which $\left(\dfrac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)^{n} = 1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

Let $S=\{\,z=x+iy:\ |z-1+i|\ge |z|,\ |z|<2,\ |z+i|=|z-1|\,\}$. Then the set of all values of $x$, for which $w=2x+iy\in S$ for some $y\in\mathbb{R}$, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Evening Shift) PYQ

Solution

Qus : 49 JEE MAIN PYQ

Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1|=9$ and $|z_2-3-4i|=4$. Then the minimum value of $|z_1-z_2|$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Evening Shift) PYQ

Solution

Qus : 50 JEE MAIN PYQ

Let a complex number z, |z| $\ne$ 1, satisfy ${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}}}} \right) \le 2$. Then, the largest value of |z| is equal to ____________.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Morning Shift) PYQ

Solution

Qus : 51 JEE MAIN PYQ

If $\alpha + i\beta$ and $\gamma + i\delta$ are the roots of $x^2 - (3 - 2i)x - (2i - 2) = 0$, $i = \sqrt{-1}$, then $\alpha \gamma + \beta \delta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Evening Shift) PYQ

Solution

Qus : 52 JEE MAIN PYQ

$\left( \dfrac{1 + \sin\frac{2\pi}{9} + i \cos\frac{2\pi}{9}}{1 + \sin\frac{2\pi}{9} - i \cos\frac{2\pi}{9}} \right)^3$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Morning) PYQ

Solution

Qus : 53 JEE MAIN PYQ

Let $p, q \in \mathbb{R}$ and $(1 - \sqrt{3}i)^{200} = 2^{199}(p + iq),\ i = \sqrt{-1}$ Then $p + q + q^2$ and $p - q + q^2$ are roots of the equation.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Morning Shift) PYQ

Solution

Qus : 54 JEE MAIN PYQ

Let $w_1$ be the point obtained by the rotation of $z_1 = 5 + 4i$ about the origin through a right angle in the anticlockwise direction, and $w_2$ be the point obtained by the rotation of $z_2 = 3 + 5i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_1 - w_2$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Morning Shift) PYQ

Solution

Qus : 55 JEE MAIN PYQ

Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z=2-i\!\left(2\tan\frac{5\pi}{8}\right)$. Then $(r,\theta)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Evening Shift) PYQ

Solution

Qus : 56 JEE MAIN PYQ

Let $A = {\theta \in [0,2\pi] : 1 + 10,\mathrm{Re}\left(\dfrac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta}\right) = 0}$. Then $\displaystyle \sum_{\theta \in A} \theta^2$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

Qus : 57 JEE MAIN PYQ

The area of the polygon, whose vertices are the non-real roots of the equation $\overline z = i{z^2}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Evening Shift) PYQ

Solution

Qus : 58 JEE MAIN PYQ

For $a \in \mathbb{C}$, let $A = \{\, z \in \mathbb{C} : \Re(a + \bar z) > \Im(\bar a + z) \,\}$ and $B = \{\, z \in \mathbb{C} : \Re(a + \bar z) < \Im(\bar a + z) \,\}$. Then among the two statements: (S1): If $\Re(a), \Im(a) > 0$, then the set $A$ contains all the real numbers. (S2): If $\Re(a), \Im(a) < 0$, then the set $B$ contains all the real numbers.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Evening Shift) PYQ

Solution

Qus : 59 JEE MAIN PYQ

If $\alpha$ and $\beta$ be the roots of the equation $x^2-2x+2=0$, then the least value of $n$ for which $\left(\dfrac{\alpha}{\beta}\right)^n=1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 60 JEE MAIN PYQ

The least value of |z| where z is complex number which satisfies the inequality $\exp \left( {{{(|z| + 3)(|z| - 1)} \over {||z| + 1|}}{{\log }_e}2} \right) \ge {\log _{\sqrt 2 }}|5\sqrt 7 + 9i|,i = \sqrt { - 1} $, is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 61 JEE MAIN PYQ

Let $z$ be a complex number such that $\lvert z+2\rvert=1$ and $\operatorname{Im}!\left(\dfrac{z+1}{z+2}\right)=\dfrac{1}{5}$. Then the value of $\lvert \operatorname{Re}(z+2)\rvert$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 62 JEE MAIN PYQ

The imaginary part of
$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$$ can be

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Evening) PYQ

Solution

Qus : 63 JEE MAIN PYQ

If $z=x+iy$ with $xy\ne0$ satisfies $z^{2}+i\overline{z}=0$, then $|z^{2}|$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Morning Shift) PYQ

Solution

Qus : 64 JEE MAIN PYQ

The value of $\left(\dfrac{\,1+\sin\frac{2\pi}{9}+i\cos\frac{2\pi}{9}\,}{\,1+\sin\frac{2\pi}{9}-i\cos\frac{2\pi}{9}\,}\right)^{3}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Evening Shift) PYQ

Solution

Qus : 65 JEE MAIN PYQ

If the set $R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}$ has $m$ elements and $\sum_\limits{n=1}^m\left(1-i^{n !}\right)=x+i y$, where $i=\sqrt{-1}$, then the value of $m+x+y$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 66 JEE MAIN PYQ

Let $z\in\mathbb{C}$, the set of complex numbers. Then the equation $2|z+3i|-|z-i|=0$ represents :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 67 JEE MAIN PYQ

If $z=\dfrac{\sqrt{3}}{2}+\dfrac{i}{2}\ \ (i=\sqrt{-1})$, then $\left(1+iz+z^{5}+iz^{8}\right)^{9}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Evening Shift) PYQ

Solution

Qus : 68 JEE MAIN PYQ

The number of points of intersection of $|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, z $\in$ C, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Evening Shift) PYQ

Solution

Qus : 69 JEE MAIN PYQ

If $z = \dfrac{1}{2} - 2i$ is such that $|z + 1| = \alpha z + \beta (1 + i)$, $i = \sqrt{-1}$ and $\alpha, \beta \in \mathbb{R}$, then $\alpha + \beta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 70 JEE MAIN PYQ

If $z$ is a complex number, then the number of common roots of $z^{1985}+z^{100}+1=0$ and $z^{3}+2z^{2}+2z+1=0$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Evening Shift) PYQ

Solution

Qus : 71 JEE MAIN PYQ

Let $C$ be the circle in the complex plane with centre $z_0=\tfrac{1}{2}(1+3i)$ and radius $r=1$. Let $z_1=1+i$ and the complex number $z_2$ be outside the circle $C$ such that $\lvert z_1-z_0\rvert\,\lvert z_2-z_0\rvert=1$. If $z_0,z_1$ and $z_2$ are collinear, then the smaller value of $\lvert z_2\rvert^2$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (12 April Morning Shift) PYQ

Solution

Qus : 72 JEE MAIN PYQ

Let $z_{1}=2+3i$ and $z_{2}=3+4i$. The set $S=\left\{\,z\in\mathbb{C}:\ |z-z_{1}|^{2}-|z-z_{2}|^{2}=|z_{1}-z_{2}|^{2}\,\right\}$ represents a

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Morning Shift) PYQ

Solution

Qus : 73 JEE MAIN PYQ

The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 74 JEE MAIN PYQ

Let $S_1, S_2$ and $S_3$ be three sets defined as $S_1 = \{z \in C : |z - 1| \le \sqrt{2}\}$ ,$S_2 = \{z \in C : \text{Re}((1 - i)z) \ge 1\}$ $S_3 = \{z \in C : \text{Im}(z) \le 1\}$ Then the set $S_1 \cap S_2 \cap S_3$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

Qus : 75 JEE MAIN PYQ

The equation $\operatorname{Im}\left( \dfrac{iz - 2}{z - i} \right) + 1 = 0,; z \in \mathbb{C},; z \neq i$ represents a part of a circle having radius equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

Qus : 76 JEE MAIN PYQ

Let $z$ be a complex number such that $\left|\dfrac{z-2i}{z+i}\right|=2,\ z\ne -i$. Then $z$ lies on the circle of radius $2$ and centre:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 77 JEE MAIN PYQ

Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z = 2 - i\left(2\tan\dfrac{5\pi}{8}\right)$, then $(r, \theta)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 78 JEE MAIN PYQ

The fractional part of the number $\dfrac{4^{2022}}{15}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Morning Shift) PYQ

Solution

Qus : 79 JEE MAIN PYQ

All the points in the set
$S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )$ lie on a :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Morning Shift) PYQ

Solution

Qus : 80 JEE MAIN PYQ

If $\mathop {\lim }\limits_{x \to 0} {{{{\sin }^{ - 1}}x - {{\tan }^{ - 1}}x} \over {3{x^3}}}$ is equal to L, then the value of (6L + 1) is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 81 JEE MAIN PYQ

If the equation $a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$ represents a circle where a, d are real constants then which of the following condition is correct?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 82 JEE MAIN PYQ

Let $S=\{\,z\in\mathbb{C}:\ \overline{z}=i\big(z^2+\operatorname{Re}(\overline{z})\big)\,\}$. Then $\displaystyle \sum_{z\in S}|z|^2$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Evening Shift) PYQ

Solution

Qus : 83 JEE MAIN PYQ

Let $z$ be a complex number such that $|z| = 1$. If $\dfrac{2 + k\bar{z}}{k + z} = kz$, $k \in \mathbb{R}$, then the maximum distance of $k + ik^2$ from the circle $|z - (1 + 2i)| = 1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

Qus : 84 JEE MAIN PYQ

For two non-zero complex numbers $z_{1}$ and $z_{2}$, if $\operatorname{Re}(z_{1}z_{2})=0$ and $\operatorname{Re}(z_{1}+z_{2})=0$, then which of the following are possible? A. $\operatorname{Im}(z_{1})>0$ and $\operatorname{Im}(z_{2})>0$ B. $\operatorname{Im}(z_{1})<0$ and $\operatorname{Im}(z_{2})>0$ C. $\operatorname{Im}(z_{1})>0$ and $\operatorname{Im}(z_{2})<0$ D. $\operatorname{Im}(z_{1})<0$ and $\operatorname{Im}(z_{2})<0$ Choose the correct answer from the options given below:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Morning Shift) PYQ

Solution

Qus : 85 JEE MAIN PYQ

A value of $\theta$ for which $ \displaystyle \frac{2 + 3i \sin \theta}{1 - 2i,} \cdot \frac{1}{\sin \theta} $ is purely imaginary, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 86 JEE MAIN PYQ

Let $z$ be a complex number such that the real part of $\displaystyle \frac{z-2i}{z+2i}$ is zero. Then, the maximum value of $\lvert z-(6+8i)\rvert$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Evening Shift) PYQ

Solution

Qus : 87 JEE MAIN PYQ

Let $z\in\mathbb{C}$ be such that $|z|<1$. If $\omega=\dfrac{5+3z}{5(1-z)},z$, then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 88 JEE MAIN PYQ

Let a complex number be w = 1 $-$ ${\sqrt 3 }$i. Let another complex number z be such that |zw| = 1 and arg(z) $-$ arg(w) = ${\pi \over 2}$. Then the area of the triangle with vertices origin, z and w is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Evening Shift) PYQ

Solution

Qus : 89 JEE MAIN PYQ

Let the solution curve of the differential equation

$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $, $y(1) = 3$ be $y = y(x)$. Then y(2) is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

Qus : 90 JEE MAIN PYQ

Let $\alpha$ and $\beta$ be the roots of the equation x² + (2i $-$ 1) = 0. Then, the value of |$\alpha$⁸ + $\beta$⁸| is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

Qus : 91 JEE MAIN PYQ

If z₁, z₂ are complex numbers such that Re(z₁) = |z₁ – 1|, Re(z₂) = |z₂ – 1| , and arg(z₁ - z₂) = ${\pi \over 6}$, then Im(z₁ + z₂) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 92 JEE MAIN PYQ

If $\alpha$ and $\beta$ are the distinct roots of the equation ${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$, then the value of ${\alpha ^{96}}({\alpha ^{12}} - 1) + {\beta ^{96}}({\beta ^{12}} - 1)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

Qus : 93 JEE MAIN PYQ

If the set $\left\{\operatorname{Re}\!\left(\dfrac{z-\overline{z}+z\overline{z}}{\,2-3z+5\overline{z}\,}\right): z\in\mathbb{C},\ \operatorname{Re}(z)=3\right\}$ is equal to the interval $(\alpha,\beta]$, then $24(\beta-\alpha)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (15 April Morning Shift) PYQ

Solution

Qus : 94 JEE MAIN PYQ

If z is a complex number such that ${{z - i} \over {z - 1}}$ is purely imaginary, then the minimum value of | z $-$ (3 + 3i) | is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

Qus : 95 JEE MAIN PYQ

Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^{3}+z_2^{3}=20+15i$. Then, $\,\big|z_1^{4}+z_2^{4}\big|\,$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 96 JEE MAIN PYQ

The point represented by $2 + i$ in the Argand plane moves $1$ unit eastwards, then $2$ units northwards and finally from there $2\sqrt{2}$ units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 97 JEE MAIN PYQ

Let $\alpha$ be a root of the equation 1 + x² + x⁴ = 0. Then, the value of $\alpha$¹⁰¹¹ + $\alpha$²⁰²² $-$ $\alpha$³⁰³³ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 98 JEE MAIN PYQ

Let $u = {{2z + i} \over {z - ki}}$, z = x + iy and k > 0. If the curve represented
by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Morning) PYQ

Solution

Qus : 99 JEE MAIN PYQ

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = ${\pi \over 4}$ intersect :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 100 JEE MAIN PYQ

If $a>0$ and $z=\dfrac{(1+i)^{2}}{,a-i,}$ has magnitude $\sqrt{\dfrac{2}{5}}$, then $\overline{z}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 101 JEE MAIN PYQ

Let $S=\left\{\,z\in\mathbb{C}:\ |z-1|=1 \ \text{and}\ \left|(\sqrt2-1)(z+\bar z)-i(z-\bar z)\right|=2\sqrt2\,\right\}$. Let $z_1,z_2\in S$ be such that $|z_1|=\max_{z\in S}|z|$ and $|z_2|=\min_{z\in S}|z|$. Then $\ \left|\sqrt2\,z_1-z_2\right|^{2}$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

Qus : 102 JEE MAIN PYQ

If the real part of the complex number ${(1 - \cos \theta + 2i\sin \theta )^{ - 1}}$ is ${1 \over 5}$ for $\theta \in (0,\pi )$, then the value of the integral $\int_0^\theta {\sin x} dx$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Evening Shift) PYQ

Solution

Qus : 103 JEE MAIN PYQ

Let $z_1, z_2$ and $z_3$ be three complex numbers on the circle $|z|=1$ with $\arg(z_1)=-\frac{\pi}{4}$, $\arg(z_2)=0$ and $\arg(z_3)=\frac{\pi}{4}$. If $\left|\,z_1\overline{z_2}+z_2\overline{z_3}+z_3\overline{z_1}\,\right|^2=\alpha+\beta\sqrt{2}$, $\alpha,\beta\in\mathbb{Z}$, then the value of $\alpha^2+\beta^2$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 104 JEE MAIN PYQ

The real part of the complex number ${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 105 JEE MAIN PYQ

The real part of the complex number ${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$ is equal to :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 106 JEE MAIN PYQ

If a and b are real numbers such that ${\left( {2 + \alpha } \right)^4} = a + b\alpha$ where $\alpha = {{ - 1 + i\sqrt 3 } \over 2}$ then a + b is equal to :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Evening) PYQ

Solution

Qus : 107 JEE MAIN PYQ

Let $z \in \mathbb{C}$ be such that $\dfrac{z^2+3i}{z-2+i}=2+3i$. Then the sum of all possible values of $z^2$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Morning Shift) PYQ

Solution

Qus : 108 JEE MAIN PYQ

If $z$ is a complex number such that $|z|\le1$, then the minimum value of $\left|z+\dfrac{1}{2}(3+4i)\right|$ is:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Evening Shift) PYQ

Solution

Qus : 109 JEE MAIN PYQ

If $z_1,z_2,z_3\in\mathbb{C}$ are the vertices of an equilateral triangle whose centroid is $z_0$, then $\displaystyle \sum_{k=1}^{3}(z_k-z_0)^2$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 110 JEE MAIN PYQ

Let $z_{0}$ be a root of the quadratic equation $x^{2}+x+1=0$. If $z=3+6i\,z_{0}^{81}-3i\,z_{0}^{93}$, then $\arg z$ is equal to:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 111 JEE MAIN PYQ

Let n denote the number of solutions of the equation z² + 3$\overline z $ = 0, where z is a complex number. Then the value of $\sum\limits_{k = 0}^\infty {{1 \over {{n^k}}}} $ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (22 July Evening Shift) PYQ

Solution

Qus : 112 JEE MAIN PYQ

If the four complex numbers $z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$ and $z-2Re(z)$ represent the vertices of a square ofside 4 units in the Argand plane, then $|z|$ is equal to :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

Solution

Qus : 113 JEE MAIN PYQ

For $z \in \mathbb{C}$ if the minimum value of $\lvert z - 3\sqrt{2}\rvert + \lvert z - p\sqrt{2}i\rvert$ is $5\sqrt{2}$, then a value of $p$ is ________.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Evening Shift) PYQ

Solution

Qus : 114 JEE MAIN PYQ

For all $z\in\mathbb{C}$ on the curve $\mathcal{C}_1:\ |z|=4$, let the locus of the point $z+\dfrac{1}{z}$ be the curve $\mathcal{C}_2$. Then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Morning Shift) PYQ

Solution

Qus : 115 JEE MAIN PYQ

If $z$ and $w$ are two complex numbers such that $|zw|=1$ and $\arg(z)-\arg(w)=\dfrac{\pi}{2}$, then:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 116 JEE MAIN PYQ

Let the curve $z(1+i)+\overline{z}(1-i)=4,\ z\in\mathbb{C}$, divide the region $|z-3|\le 1$ into two parts of areas $\alpha$ and $\beta$. Then $|\alpha-\beta|$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

Qus : 117 JEE MAIN PYQ

The equation $|z - i| = |z - 1|$, where $i = \sqrt{-1}$, represents :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution

Qus : 118 JEE MAIN PYQ

The value of ${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Evening) PYQ

Solution

Qus : 119 JEE MAIN PYQ

Let $O$ be the origin and $A$ be the point $z_1 = 1 + 2i$. If $B$ is the point $z_2$, $\mathrm{Re}(z_2) < 0$, such that $OAB$ is a right-angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Morning Shift) PYQ

Solution

Qus : 120 JEE MAIN PYQ

Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3|z_1| = 4|z_2|.$ If $z = \dfrac{3z_1}{2z_2} + \dfrac{2z_2}{3z_1}$, then :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

Solution

Qus : 121 JEE MAIN PYQ

A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\dfrac{z_{1}-2z_{2}}{2-z_{1}\overline{z_{2}}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

Qus : 122 JEE MAIN PYQ

If the center and radius of the circle $\left|\dfrac{z-2}{z-3}\right|=2$ are respectively $(\alpha,\beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Morning Shift) PYQ

Solution

Qus : 123 JEE MAIN PYQ

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, z \in C$, be the equation of a circle with center at $C$. If the area of the triangle, whose vertices are at the points $(0,0), C$ and $(\alpha, 0)$ is 11 square units, then $\alpha^2$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

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