Complex Numbers PYQs - Last 10 Years
WB JEE / Mathematics / Algebra / 31 recent questions
MathematicsAlgebra2017-2026
Practice 31 WB JEE Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2017-2026
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Last 10 Years Complex Numbers Questions
Showing 31 of 31 filtered questions.
1Complex Numbers
Let $Z_1, Z_2$ be the roots of the equation $Z^2+p Z+q=0$, where the coefficients $p$ and $q$ may be complex numbers and also let $A, B$ represent $Z_1, Z_2$ respectively in the complex plane. If $\angle A O B=\alpha \neq 0$ and $O A=O B$, ...
MCQ+2 / -0.52026
2Complex Numbers
The total number of polynomials of the form $x^3+a x^2+b x+c$ which is divisible by $x^2+1$, where $a, b, c \in\{1,2,3, \ldots ., 10\}$ is
MCQ+1 / -0.252026
3Complex Numbers
The expression $\sum_{k=1}^{32}(3 K+2)\left\{\sum_{r=1}^{10}\left(\sin \frac{2 r \pi}{11}-i \cos \frac{2 r \pi}{11}\right)\right\}^k$ represents
MCQ+1 / -0.252026
4Complex Numbers
Let $\omega(\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\left\{\mid a+b \omega+c \omega^2\right\}^2 ; a, b, c$ are distinct non-zero integers} equals
MCQ+1 / -0.252025
5Complex Numbers
If $\left|Z_1\right|=\left|Z_2\right|=\left|Z_3\right|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose vertices are $Z_1, Z_2, Z_3$ is
MCQ+2 / -0.52025
6Complex Numbers
If $z_1, z_2$ are complex numbers such that $\frac{2 z_1}{3 z_2}$ is a purely imaginary number, then the value of $\left|\frac{z_1-z_2}{z_1+z_2}\right|$ is
MCQ+1 / -0.252025
7Complex Numbers
If \(\cos \theta+i \sin \theta, \theta \in \mathbb{R}\), is a root of the equation
\(a_0 x^n+a_1 x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots . a_n \in \mathbb{R}, a_0 \neq 0,\)
then the value of $$a_1 \sin \theta+a_2 \sin 2 \theta+\l...
\(a_0 x^n+a_1 x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots . a_n \in \mathbb{R}, a_0 \neq 0,\)
then the value of $$a_1 \sin \theta+a_2 \sin 2 \theta+\l...
MCQ+1 / -0.252024
8Complex Numbers
If \(z_1\) and \(z_2\) be two roots of the equation \(z^2+a z+b=0, a^2<4 b\), then the origin, \(\mathrm{z}_1\) and \(\mathrm{z}_2\) form an equilateral triangle if
MCQ+1 / -0.252024
9Complex Numbers
If z\(_1\) and z\(_2\) are two complex numbers satisfying the equation \(\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}} \right| = 1\), then \({{{z_1}} \over {{z_2}}}\) may be
MCQM+2 / -02023
10Complex Numbers
Reflection of the line \(\overline a z + a\overline z = 0\) in the real axis is given by :
MCQ+1 / -0.252023
11Complex Numbers
If the vertices of a square are \({z_1},{z_2},{z_3}\) and \({z_4}\) taken in the anti-clockwise order, then \({z_3} =\)
MCQ+1 / -0.252023
12Complex Numbers
Let z1 and z2 be two non-zero complex numbers. Then
MCQM+2 / -02022
13Complex Numbers
If z = x \(-\) iy and \({z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)\), then \({{\left( {{x \over p} + {y \over q}} \right)} \over {({p^2} + {q^2})}}\) is equal to
MCQ+1 / -0.252022
14Complex Numbers
If \(|z - 25i| \le 15\), then Maximum arg(z) \(-\) Minimum arg(z) is equal to
(arg z is the principal value of argument of z)
(arg z is the principal value of argument of z)
MCQ+1 / -0.252022
15Complex Numbers
If \(\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0\) for a complex number z, then z is equal to
MCQM+2 / -02021
16Complex Numbers
Let C denote the set of all complex numbers. Define A = {(z, w) | z, w\(\in\)C and |z| = |w|}, B = {z, w} | z, w\(\in\)C and z2 = w2}. Then
MCQ+1 / -0.252021
17Complex Numbers
If |z| = 1 and z \(\ne\) \(\pm\) 1, then all the points representing \({z \over {1 - {z^2}}}\) lie on
MCQ+1 / -0.252021
18Complex Numbers
The number of complex numbers p such that \(\left| p \right| = 1\) and imaginary part of p4 is 0, is
MCQ+1 / -0.252020
19Complex Numbers
The equation \(z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0\) represents a circle of radius
MCQ+1 / -0.252020
20Complex Numbers
The general value of the real angle \(\theta\), which satisfies the equation, \((\cos \theta + i\sin \theta )(\cos 2\theta + i\sin 2\theta )...(\cos n\theta + i\sin n\theta ) = 1\) is given by, (assuming k is an integer)
MCQ+1 / -0.252019
21Complex Numbers
Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z \(-\) arg(\(-\) z) is
MCQ+1 / -0.252019
22Complex Numbers
The polar coordinate of a point P is \(\left( {2, - {\pi \over 4}} \right)\). The polar coordinate of the point Q which is such that line joining PQ is bisected perpendicularly by the initial line, is
MCQ+2 / -0.52019
23Complex Numbers
For any non-zero complex number z, the minimum value of | z | + | z \(-\) 1 | is
MCQ+2 / -0.52019
24Complex Numbers
If \(\theta \in R\) and \({{1 - i\cos \theta } \over {1 + 2i\cos \theta }}\) is real number, then \(\theta\) will be (when I : Set of integers)
MCQM+2 / -02019
25Complex Numbers
If \({Z_r} = \sin {{2\pi r} \over {11}} - i\cos {{2\pi r} \over {11}}\), then \(\sum\limits_{r = 0}^{10} {{Z_r}}\) is equal to
MCQ+1 / -0.252018
26Complex Numbers
If z1 and z2 be two non-zero complex numbers such that \({{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1\), then the origin and the points represented by z1 and z2
MCQ+1 / -0.252018
27Complex Numbers
Let z1 and z2 be complex numbers such that z1 \(\ne\) z2 and |z1| = |z2|. If Re(z1) > 0 and Im(z2) < 0, then \({{{z_1} + {z_2}} \over {{z_1} - {z_2}}}\) is
MCQ+2 / -0.52018
28Complex Numbers
If \({a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}\), then the value of \(\left| {\matrix{
{{a_1}} & {{a_2}} & {{a_3}} \cr
{{a_4}} & {{a_5}} & {{a_6}} \cr
{{a_7}} & {{a_8}} & {{a_9}} \cr
} } \right|\) is equal to
MCQ+1 / -0.252018
29Complex Numbers
The expression \({{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}\) equals
MCQ+1 / -0.252017
30Complex Numbers
Let z = x + iy, where x and y are real. The points (x, y) in the X-Y plane for which \({{{z + i} \over {z - i}}}\) is purely imaginary, lie on
MCQ+1 / -0.252017
31Complex Numbers
The complex number z satisfying the equation | z \(-\) 1 | = | z + 1 | = 1 is
MCQM+2 / -02017