Complex Numbers · Mathematics · WB JEE

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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
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