Question Text
Question 3 :
If $z = \displaystyle \frac{(3 + 4i)(5 - 7 i)}{(7 + 5i)(4 - 3i)}$ then $|z| = ?$
Question 4 :
<span>Find the value of $\displaystyle \left( 4+2i \right) \left( 4-2i \right) $ given</span> that $\displaystyle { i }^{ 2 }=-1$. 
Question 5 :
What is the modulus of $\cfrac { \sqrt { 2 } +i }{ \sqrt { 2 } -i } $ where $i=\sqrt { -1 } $
Question 7 :
Find the value of $x$ of the equation ${ \left( 1-i \right)  }^{ x }={ 2 }^{ x }$ 
Question 9 :
$\displaystyle \left ( \frac{1 + i}{1 - i} \right )^2 + \left(\frac{1 - i}{1 + i} \right )^2$ is equal to
Question 10 :
 If $z_1=\sqrt { 3 } -i,z_2=1+i\sqrt { 3 } ,$ then amp$(z_1+z_2)=$ 
Question 13 :
If arg $\left( {{Z_1} + {Z_2}} \right) = 0\;$ and $|{z_1}|\; = \;|{z_2}|\; = 1.$ then.
Question 15 :
The number of non-zero integral solutions of the equation ${ \left| 1-i \right| }^{ x }={ 2 }^{ x }$, is
Question 19 :
Find the value of $\begin{vmatrix} 2+i & 2-i \\ 1+i & 1-i \end{vmatrix}$ if $i^2=-1$.
Question 22 :
If $i^{2} = -1$, calculate the value of $3i^{2} + i^{3} - i^{4}$.
Question 24 :
If $z=x+iy(x,y\epsilon R,x\neq -1/2),$ the number of values of z satisfying $\left | z \right |^{n}=z^{2}\left | z \right |^{n-2}+1.(n\epsilon N,n> 1)$is
Question 25 :
If $z$ is a complex number such that $|z|=1$, then $\left|\dfrac 1{\bar z}\right|$ is 
Question 29 :
Let $n$ be a positive integer. Then $\left ( i \right )^{4n+1}+\left ( -i \right )^{4n+5}=$