Q.1
Let z = x + iy be the complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $\bar{z} z^3 + z (\bar{z})^3 =350$ is
  • 48
  • 32
  • 40
  • 80
Q.2
if $ z= \left ( \frac {\sqrt 3 + i}{2} \right )^5 + \left ( \frac {\sqrt 3 - i}{2} \right )^5$ , then
  • Re(z) =0
  • Im (z) =0
  • Re(z), Im(z) > 0
  • Re(z) > 0, Im(z) < 0
Q.3
if |z| =1 and $ z \ne 1$ , then all the values of $\frac {z}{1-z^2} $ lie on
  • x axis
  • y axis
  • $|z| = \sqrt 2$
  • A line not passing through the origin
Q.4
if |z|=1 and $\omega = \frac {z-1}{z+1}$ ( where $z \ne -1$ Then $Re( \omega )$ is
  • 0
  • $- \frac {1}{|z+1|^2}$
  • $|\frac {z}{z+1}|. \frac {1}{|z+1\^2}$
  • $ \frac {\sqrt 2}{|z+1|^2}$
Q.5
If $ z_1$ ,$z_2$ ,$z_3$ are complex numbers such that $| z_1| = | z_2|=| z_3| = | \frac {1}{z_1} + \frac {1}{z_2} +\frac {1}{z_3}|=1$,then $|z_1 + z_2 + z_3|$ is
  • 1
  • < 1
  • > 1
  • 3
Q.6
The area of the triangle on the complex plane formed by the complex numbers z, – iz and z + iz is
  • $|z|^2$
  • $| \bar{z}|^2$
  • $\frac {|z|^2}{2}$
  • $\frac {|z|^2}{4}$
Q.7
The value of arg (x) when x < 0 is:
  • 0
  • $\frac {\pi}{2}$
  • $\pi$
  • none of these
Q.8
if  $\omega$ ( $\ne 1$) is a cube root of the unity and $(1 + \omega )^7 = A + B \omega $, then A and B are respectively the numbers
  • 0,1
  • 1,1
  • 1,0
  • -1 ,1
Q.9
sinx + i cos 2x and cos x – i sin 2x are conjugate to each other for
  • $x = n \pi$
  • x=0
  • $x = (n + \frac {1}{2}) \frac {\pi}{2}$
  • No value of x
Q.10
The point $z_1$, $z_2$, $z_3$,$z_4$ in the complex plane are the vertices of a parallelogram taken in order if and only if
  • $z_1 +z_4 =z_2 + z_3$
  • $z_1 +z_2=z_3 + z_4$
  • $z_1 +z_3 =z_2 + z_4$
  • None of these
Q.11
What is the smallest positive integer n, for which $(1 + i)^2n = (1 – i)^2n$?
  • 2
  • 3
  • 4
  • 8
Q.12
if $z_1 = a+ ib$ and $z_2 =c+ id$ such that $|z_1|= |z_2|=1$ and $Re(z_1 \bar{z_2}) =0$, then the pair of the  complex number $W_1=a+ic$ and $W_2 =b+id$ satisfies
  • $|W_1|=1$
  • $|W_2|=1$
  • $Re(W_1 \bar{W_2}) =0$
  • All the above
Q.13
For all complex  numbers $z_1$ ,$z_2$ satisfying $|z_1| =12$ and $|z_2 -3 -4i|=5$, the minimum value of $|z_1 -z_2|$ is
  • 0
  • 2
  • 7
  • 17
0 h : 0 m : 1 s