Question 1 :
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 3 :
$\displaystyle \frac{\displaystyle i^{4n + 3} + (-i)^{8n - 3}}{\displaystyle(i)^{12 n- 1} - i^{2 - 16 n}}, n \varepsilon N$ is equal to

Question 4 :
Which of the the following is correct representation of the complex number: $(a,b)$

Question 5 :
Let P$\left( x \right) ={ x }^{ 3 }-6{ x }^{ 2 }+Bx+C$ has 1+5i as a zero and B,C real number, then value of (B+C) is

Question 6 :
The value of ${\left( {1 + i} \right)^5} \times {\left( {1 - i} \right)^5}$ is

Question 10 :
$i^n + i^{n + 1} + i^{n + 2}+ i^{n + 3} (n   \in   N) $ is equal to

Question 15 :
If $\cos { \left( \log { { i }^{ 4i } }  \right)  } =a+ib$, then

Question 16 :
Inequality $a + i b > c + i d$ can be explained only when :

Question 17 :
The real part of $\left[ 1 + \cos \left( \dfrac { \pi } { 5 } \right) + i \sin \left( \dfrac { \pi } { 5 } \right) \right] ^ { - 1 }$ is

Question 19 :
Let $\left| z _ { i } \right| = i , i = 1,2,3,4$ and $\left| 16 z _ { 1 } z _ { 2 } z _ { 3 } + 9 z _ { 1 } z _ { 2 } z _ { 4 } + 4 z _ { 1 } z _ { 3 } z _ { 4 } + z _ { 2 } z _ { 3 } z _ { 4 } \right| = 48 ,$ then the value of $\left| \dfrac { 1 }{ \overline { z } _{ { 1 } } } +\dfrac { 4 }{ \overline { z } _{ { 2 } } } +\dfrac { 9 }{ \overline { z } _{ { 3 } } } +\dfrac { 16 }{ \overline { z } _{ { 4 } } } \right| .$

Question 20 :
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