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## MCQ (More than One Correct Answer)

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Let z1 and z2 be two non-zero complex numbers. Then
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If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equa...
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If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right)... WB JEE 2022 If$$|z - 25i| \le 15$$, then Maximum arg(z)$$-$$Minimum arg(z) is equal to (arg z is the principal value of argument ... WB JEE 2022 Let C denote the set of all complex numbers. Define A = {(z, w) | z, w$$\in$$C and |z| = |w|}, B = {z, w} | z, w$$\in$$C... WB JEE 2021 If |z| = 1 and z$$\ne\pm$$1, then all the points representing$${z \over {1 - {z^2}}}$$lie on WB JEE 2021 The equation$$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$represents a circle of radius WB JEE 2020 The number of complex numbers p such that$$\left| p \right| = 1$$and imaginary part of p4 is 0, is WB JEE 2020 If$$\omega\ne$$1 is a cube root of unity, then the sum of the series$$S = 1 + 2\omega + 3{\omega ^2} + \,\,.......
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If $$x + {1 \over x} = 2\cos \theta$$, then for any integer n, $${x^n} + {1 \over {{x^n}}} =$$
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For the real parameter t, the locus of the complex number $$z = (1 - {t^2}) + i\sqrt {1 + {t^2}}$$ in the complex plane...
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If $$- \pi WB JEE 2010 If$$z = {4 \over {1 - i}}$$, then$$\overline z $$is (where$$\overline z $$is complex conjugate of z) WB JEE 2010 For any complex number z, the minimum value of$$|z| + |z - 1|$$is WB JEE 2009 The modulus of$${{1 - i} \over {3 + i}} + {{4i} \over 5}$$is WB JEE 2009 If$$i = \sqrt { - 1} $$and n is positive integer, then$${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}}$$is equal to... WB JEE 2009 If 1,$$\omega$$,$$\omega$$2 are cube roots of unity, then$$\left| {\matrix{ 1 & {{\omega ^n}} & {{\omega ^{2n}}} ...
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For two complex numbers z1, z2 the relation $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \... WB JEE 2008 A and B are two points on the Argand plane such that the segment AB is bisected at the point (0, 0). If the point A, whi... WB JEE 2008 The principal amplitude of$${(\sin 40^\circ + i\cos 40^\circ )^5}$$is WB JEE 2008 Let$$\alpha$$,$$\beta$$be the roots of$${x^2} - 2x\cos \phi + 1 = 0$$, then the equation whose roots are$${\alpha ...
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The value of $${(1 - \omega + {\omega ^2})^5} + {(1 + \omega - {\omega ^2})^5}$$, where $$\omega$$ and $$\omega$$2 are...
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## Subjective

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