Question 1 :
If $\cos { \left( \log { { i }^{ 4i } }  \right)  } =a+ib$, then
Question 3 :
The sum of two complex numbers $a + ib$ and $c+ id$ is purely imaginary if
Question 5 :
The least positive integer $n$ such that $\left ( \dfrac{1-i}{1+i} \right )^{2n}=1$ is .....
Question 6 :
The real part of $\left[ 1 + \cos \left( \dfrac { \pi } { 5 } \right) + i \sin \left( \dfrac { \pi } { 5 } \right) \right] ^ { - 1 }$ is
Question 7 :
The value of ${\left( {1 + i} \right)^5} \times {\left( {1 - i} \right)^5}$ is
Question 8 :
The complex number $e^{i\theta }$ can be expressed in vector form by
Question 10 :
If $u = 3 - 5i$ and $v = -6 + i$, then the value of $(u+v)^2$ is
Question 11 :
The value of $\displaystyle \left ( \frac{1-i}{1+i} \right )^{10}+\left ( \frac{1+i}{1-i} \right )^8=$
Question 12 :
Two complex numbers are represented by ordered pairs $z_1: a+ib\ \&\ z_2: c+id $, which of the following is correct representation for $z_1- z_2=$?
Question 13 :
The complex number system, denoted by $C$, is the set of all ordered pairs of real numbers (that is, $R \times R$) with the operations of addition (denoted by $+$) which satisfy
Question 14 :
The argument of $\displaystyle \frac{(1 - i \sqrt 3)}{(1 + i \sqrt 3)}$ is
Question 18 :
Two complex numbers are represented by ordered pairs $z_1: (2,4)\ \&\ z_2: (-4,5)$, which of the following is real part for $z_1\times z_2=$?
Question 19 :
If $\cfrac { { \left( p+i \right) }^{ 2 } }{ 2p-i } =\mu +i\lambda $, then $\mu^2+\lambda^2$ is equal to
Question 21 :
$i^n + i^{n + 1} + i^{n + 2}+ i^{n + 3} (n   \in   N) $ is equal to
Question 23 :
The roots of the equation ${ \left( z+\alpha \beta \right) }^{ 3 }={ \alpha }^{ 3 }$ represent the vertices of a triangle, one of whose sides is of length
Question 27 :
The simplest form of the expression $\dfrac {10 - \sqrt {-12}}{1 - \sqrt {-27}} $ is
Question 28 :
If $i^2$ $= -1$, then find the odd one out of the following expressions.
Question 29 :
A complex number is represented by an ordered pair $z: (3,4)$, which of the following is true for $z$?
Question 31 :
If $ z = \dfrac {-1}{2} + i \dfrac {\sqrt3}{2} $, then $ 8 + 10z + 7z^2 $ is equal to :
Question 33 :
For two non-zero complex number $A$ & $B$ if $A + \dfrac{1}{B} = \overline A $ and $\dfrac{1}{A} + B = \overline B $ then-
Question 34 :
If $|z-3+2i|\le 4$ (where $i=\sqrt {-1})$ then the difference of greatest and least value of $|z|$ is 
Question 35 :
If $z$ is a complex number such that $z + |z| = 8 + 12i$, then the value of $|z^{2}|$ is
Question 36 :
$I_m$ $\left( {\sqrt {a + i\sqrt {{a^4} + {a^2} + 1} } } \right) = $
Question 37 :
The multiplicative inverse of the complex number $ 503−4i$ is $x+iy$ the value of $x$ is
Question 38 :
If $z + \sqrt {2}|z + 1| + i = 0$ and $z = x + iy$, then
Question 39 :
Two complex numbers are represented by ordered pairs $z_1: (a,0)\ \&\ z_2: (c,d)$, which of the following is correct simplification for $z_1\times z_2=$?
Question 41 :
Assertion: Statement -1: If $z_1$ and $z_2$ are two complex numbers such that $|z_1| = |z_2| + |z_1 - z_2|$, then $Im \left ( \frac{z_1}{z_2} \right )=0$
Reason: Statement -2: $ arg(z) = 0 \Rightarrow z$ is purely real.
Question 43 :
What is ${ i }^{ 1000 }+{ i }^{ 1001 }+{ i }^{ 1002 }+{ i }^{ 1003 }$ equal to (where $i=\sqrt { -1 } $)?
Question 44 :
If $|2z-1|=|z-2|$ and $z_1, z_2, z_3$ are complex numbers such that $|z_1-\alpha| < \alpha, |z_2-\beta| < \beta$, then $|\displaystyle \frac {z_1+z_2}{\alpha+\beta}|$
Question 45 :
If $\dfrac { z+1 }{ z+i }$ is purely imaginary, then z lies on a 
Question 47 :
For two unimodular complex numbers $z_1$ and $z_2$, $\begin{bmatrix} \overline z_1& -z_2 \\ \overline z_2 & z_1\end{bmatrix}^{-1}$ <br> $\begin{bmatrix} z_1& z_2 \\ -\overline z_2 & \overline z_1\end{bmatrix}^{-1}$ is equal to
Question 48 :
If $(\sqrt 3-i)^n=2^n, n\in N$, then $n$ is a multiple of<br/>
Question 49 :
The value of $z$ satisfying the equation $\log z+\log z^2+.....+\log z^n=0$ is
Question 50 :
If '$\omega$' is a complex cube root of unity,then $\omega ^{ \begin{pmatrix} \frac { 1 }{ 3 } & +\frac { 2 }{ 9 } +\frac { 4 }{ 27 } ...\infty \end{pmatrix} }+\omega^{ \begin{pmatrix} \frac { 1 }{ 2 } & +\frac { 3 }{ 8 } +\frac { 9 }{ 32 } ...\infty \end{pmatrix} }=$
