The multiplicative inverse of  $(2 +  \sqrt {3} i)^2$ is
  • $ \frac {1}{49} + \frac {4 \sqrt 3}{49} i$
  • $ \frac {1}{49} - \frac {4 \sqrt 3}{49} i$
  • $ \frac {1}{49} + \frac { \sqrt 3}{49} i$
  • $ \frac {1}{48} + \frac { \sqrt 3}{12} i$
The conjugate of  $ \frac { 2-i}{(1 -2i)^2}$ is
  • $ \frac {-2}{25} – i \frac {11}{25}$
  • $ \frac {-2}{25} + i \frac {11}{25}$
  • $ \frac {-2}{5} – i \frac {11}{5}$
  • $ \frac {-2}{5} + i \frac {11}{5}$
The least positive value of n if $(\frac {1+i}{1-i})^4 =1$ is
  • 2
  • 3
  • 4
  • 8
If z is a complex number, then
  • |z2| >|z|2
  • |z2| =|z|2
  • |z2| < |z|2
  • $|z^2| \geq |z|^2$
The modules of $(2-i)^6$ is
  • 25
  • 5
  • 125
  • $\sqrt {5}$
Complex number restricted by the below equation will lie on |z-1| = |z+1|
  • Parabola
  • Circle
  • Ellipse
  • Straight line
The real value of $\theta$ for which the expression $\frac {1 +  i cos \theta}{1 -2i cos \theta}$  is a real number is
  • $ n \pi + \frac {\pi}{4}$
  • $ n \pi \pm \frac {\pi}{2}$
  • $ n \pi + (-1)^n \frac {\pi}{4}$
  • None of these
Match the column
class11-maths-complex-numbers-mcq-1.png
  • p -> iv, q -> iii, r -> ii, c -> i
  • p -> iii, q -> iv, r -> i, c -> ii
  • p -> i, q -> iv, r -> ii, c -> iii
  • p -> iii, q -> iv, r -> ii, c -> i
if $z^2 =i$, then z is
  • $\pm ( \frac {1}{\sqrt 2} + ( \frac {i}{\sqrt 2}$
  • $\pm ( \frac {1}{\sqrt 2} - ( \frac {i}{\sqrt 2}$
  • $\pm ( \frac {1}{2} + ( \frac {i}{ 2}$
  • $\pm ( \frac {1}{2} - ( \frac {i}{ 2}$
The value of  $ 1 + i + i^2 + i^3 + i^4 + i^5 + i^6 + i^7$ is
  • 1
  • -1
  • 2
  • 0
The principal argument of $ \frac {-16}{1 + i \sqrt 3}$ is
  • $\frac { \pi}{3}$
  • $\frac {2 \pi}{3}$
  • $\frac { \pi}{4}$
  • $\frac {- \pi}{3}$
The amplitude of $sin \frac {\pi}{5} + i (1-   cos \frac {\pi}{5})$ is
  • $ \frac {2 \pi}{5}$
  • $ \frac { \pi}{5}$
  • $ \frac { \pi}{15}$
  • $ \frac { \pi}{10}$
The roots of quadratic equation $3x^2 + 7ix + 6=0$ is
  • 3i, 2i/3
  • 3i, -2i/3
  • -3i, -2i/3
  • -3i, 2i/3
Number of solutions of the equation $z^2 + |z|^2 = 0$ is
  • 0
  • 1
  • 2
  • infinitely many
The roots of the equation $9x^2 -12x + 20 =0$ is
  • $2 \pm 3i$
  • $ \frac {2}{3} \pm \frac {4}{3} i$
  • $ \frac {1}{3} \pm \frac {2}{3} i$
  • $3 \pm 2i$
Match the column
class11-maths-complex-numbers-mcq-2.png
  • p -> iii, q -> iv, r -> i, s -> ii
  • p -> iv, q -> iii, r -> i, s -> ii
  • p -> iii, q -> iv, r -> ii, s -> i
  • p -> i, q -> iv, r -> iii, s -> ii
if $z_1 = 1-i$ and $z_2=-1 + 2i$, then $Im(\frac {z_1z_2}{\bar{z_2}}$ is
  • 1/3
  • 2/3
  • 5/3
  • -5/3
The equation $|z + 1 -i| − = |z -1 +i|$ represents a
  • straight line
  • circle
  • parabola
  • hyperbola
0 h : 0 m : 1 s

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