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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 $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta$$ will be (...
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The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is
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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$$and imaginary part of p4 is 0, is WB JEE 2020 The polar coordinate of a point P is$$\left( {2, - {\pi \over 4}} \right)$$. The polar coordinate of the point Q which... WB JEE 2019 For any non-zero complex number z, the minimum value of | z | + | z$$-$$1 | is WB JEE 2019 The general value of the real angle$$\theta$$, which satisfies the equation,$$(\cos \theta + i\sin \theta )(\cos 2\th...
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Let z be a complex number such that the principal value of argument, arg z &gt; 0. Then, arg z $$-$$ arg($$-$$ z) is
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Let z1 and z2 be complex numbers such that z1 $$\ne$$ z2 and |z1| = |z2|. If Re(z1) &gt; 0 and Im(z2) &lt; 0, then $${... WB JEE 2018 If$${a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}$$, then the value of$$\left| {\matrix{ {{a_1}} &amp; {{a_2}} &amp;...
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If z1 and z2 be two non-zero complex numbers such that $${{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1$$, then t...
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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 e...
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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 pu...
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The expression $${{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}$$ equals
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If $$\omega$$ $$\ne$$ 1 is a cube root of unity, then the sum of the series $$S = 1 + 2\omega + 3{\omega ^2} + \,\,....... WB JEE 2011 If$$x + {1 \over x} = 2\cos \theta $$, then for any integer n,$${x^n} + {1 \over {{x^n}}} = $$WB JEE 2011 For the real parameter t, the locus of the complex number$$z = (1 - {t^2}) + i\sqrt {1 + {t^2}} $$in the complex plane... WB JEE 2011 If$$ - \pi
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If $$z = {4 \over {1 - i}}$$, then $$\overline z$$ is (where $$\overline z$$ is complex conjugate of z)
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For any complex number z, the minimum value of $$|z| + |z - 1|$$ is
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The modulus of $${{1 - i} \over {3 + i}} + {{4i} \over 5}$$ is
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If $$i = \sqrt { - 1}$$ and n is positive integer, then $${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}}$$ is equal to...
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If 1, $$\omega$$, $$\omega$$2 are cube roots of unity, then $$\left| {\matrix{ 1 & {{\omega ^n}} & {{\omega ^{2n}}} ... WB JEE 2008 For two complex numbers z1, z2 the relation$$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \...
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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...
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The principal amplitude of $${(\sin 40^\circ + i\cos 40^\circ )^5}$$ is
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Let $$\alpha$$, $$\beta$$ be the roots of $${x^2} - 2x\cos \phi + 1 = 0$$, then the equation whose roots are $${\alpha ... WB JEE 2008 The value of$${(1 - \omega + {\omega ^2})^5} + {(1 + \omega - {\omega ^2})^5}$$, where$$\omega$$and$$\omega$$2 are... WB JEE 2008 ## Subjective More Prove that if the ratio$${{z - i} \over {z - 1}} is purely imaginary, the point z lies on the circle in the Argand pl...
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