# Complex Numbers · Mathematics · WB JEE

Start Practice## MCQ (Single Correct Answer)

WB JEE 2008

The value of $${(1 - \omega + {\omega ^2})^5} + {(1 + \omega - {\omega ^2})^5}$$, where $$\omega$$ and $$\omega$$2 are the complex cube roots of uni...

WB JEE 2008

Let $$\alpha$$, $$\beta$$ be the roots of $${x^2} - 2x\cos \phi + 1 = 0$$, then the equation whose roots are $${\alpha ^n},{\beta ^n}$$ is

WB JEE 2008

The principal amplitude of $${(\sin 40^\circ + i\cos 40^\circ )^5}$$ is

WB JEE 2008

A and B are two points on the Argand plane such that the segment AB is bisected at the point (0, 0). If the point A, which is in the third quadrant ha...

WB JEE 2008

For two complex numbers z1, z2 the relation $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ holds if...

WB JEE 2008

If 1, $$\omega$$, $$\omega$$2 are cube roots of unity, then $$\left| {\matrix{
1 & {{\omega ^n}} & {{\omega ^{2n}}} \cr
{{\omega ^{2n}}} & 1 &...

WB JEE 2009

If $$i = \sqrt { - 1} $$ and n is positive integer, then $${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}}$$ is equal to

WB JEE 2009

The modulus of $${{1 - i} \over {3 + i}} + {{4i} \over 5}$$ is

WB JEE 2009

For any complex number z, the minimum value of $$|z| + |z - 1|$$ is

WB JEE 2010

If $$z = {4 \over {1 - i}}$$, then $$\overline z $$ is (where $$\overline z $$ is complex conjugate of z)

WB JEE 2010

If $$ - \pi

WB JEE 2011

For the real parameter t, the locus of the complex number $$z = (1 - {t^2}) + i\sqrt {1 + {t^2}} $$ in the complex plane is

WB JEE 2011

If $$x + {1 \over x} = 2\cos \theta $$, then for any integer n, $${x^n} + {1 \over {{x^n}}} = $$

WB JEE 2011

If $$\omega$$ $$\ne$$ 1 is a cube root of unity, then the sum of the series $$S = 1 + 2\omega + 3{\omega ^2} + \,\,.....\,\, + 3n{\omega ^{3n - 1}}$$...

WB JEE 2023

If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} = $$

WB JEE 2023

Reflection of the line $$\overline a z + a\overline z = 0$$ in the real axis is given by :

WB JEE 2022

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)

WB JEE 2022

If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right)} \over {({p^2} + {q^2})}}$$ i...

WB JEE 2021

If |z| = 1 and z $$\ne$$ $$\pm$$ 1, then all the points representing $${z \over {1 - {z^2}}}$$ lie on

WB JEE 2021

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...

WB JEE 2020

The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary part of p4 is 0, is

WB JEE 2020

The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius

WB JEE 2019

Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z $$-$$ arg($$-$$ z) is

WB JEE 2019

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...

WB JEE 2019

For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is

WB JEE 2019

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 ...

WB JEE 2018

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

WB JEE 2018

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 repre...

WB JEE 2018

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}} &...

WB JEE 2018

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} -...

WB JEE 2017

The expression $${{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}$$ equals

WB JEE 2017

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

## Subjective

WB JEE 2008

Prove that if the ratio $${{z - i} \over {z - 1}}$$ is purely imaginary, the point z lies on the circle in the Argand plane whose centre is at the poi...

## MCQ (More than One Correct Answer)

WB JEE 2023

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...

WB JEE 2022

Let z1 and z2 be two non-zero complex numbers. Then

WB JEE 2021

If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equal to

WB JEE 2019

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)

WB JEE 2017

The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is