If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = {\pi \over 2} , then :

If a > 0 and z = {{{{\left( {1 + i} \right)}^2}} \over {a - i}}, has magnitude \sqrt {{2 \over 5}}, then $$\overline{z}$$ is equal to :

Let z $$\in$$ C be such that |z| < 1. If \omega = {{5 + 3z} \over {5(1 - z)}}z, then :

All the points in the set S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} ) lie on a :

If z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right), then (1 + iz + z5 + iz8)9 is equal to :

If $$\alpha$$ and $$\beta$$ be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which {\left( {{\alpha \over \beta }} \right)^n} = 1 is :

If {{z - \alpha } \over {z + \alpha }}\left( {\alpha \in R} \right) is a purely imaginary number and | z | = 2, then a value of $$\alpha$$ is :

Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of | z1 – z2 | is :

Let $$\alpha$$ and $$\beta$$ be two roots of the equation x2 + 2x + 2 = 0 , then $${\alpha }^{15}$$ + $${\beta }^{15}$$ is equal to :

Let A = \left\{ {\theta \in \left( { - {\pi \over 2},\pi } \right):{{3 + 2i\sin \theta } \over {1 - 2i\sin \theta }}is\,purely\,imaginary} \right\} . Then the sum of the elements in A is :

Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz$${}_0^{81}$$ $$-$$ 3iz$${}_0^{93}$$, then arg z is equal to :

Let z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5}. If R(z) and 1(z) respectively denote the real and imaginary parts of z, then :

Let {\left( { - 2 - {1 \over 3}i} \right)^3} = {{x + iy} \over {27}}\left( {i = \sqrt { - 1} } \right),\,\, where x and y are real numbers, then y $$-$$ x equals :

Let z be a complex number such that |z| + z = 3 + i (where i = $$\sqrt{-1}$$). Then |z| is equal to :

Let z1 and z2 be any two non-zero complex numbers such that $$3\left|z_1\right|=4\left|z_2\right|.$$ If z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}} then :

If a tangent to the circle x2 + y2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90o, then the length (in cm) of their common chord is :

The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is :

The line x = y touches a circle at the point (1,1). If the circle also passes through the point (1, – 3), then its radius is :