Question Text
Question 1 :
Write the complete number $- 2 - 2i$ in polar form.
Question 2 :
For positive integers $n_1, n_2$ the value of the expression $(1 + i)^{n_1} + (1 + i^3)^{n_1} + (1 + i^5)^{n_2} + (1 + i^7)^{n_2} $, where $i = \sqrt{-1}$, is a real number if
Question 3 :
If $z = x+iy$ and $w = \dfrac{(1-iz)}{(z-i)}$, then $|w| = 1$ implies that, in the complex plane
Question 4 :
For positive integers $n_1, n_2, $ the value of the expression $(1 + i)^{n_1} + (1 + i^3)^{n_1} + (1 + i^5)^{n_2} + (1 + i^7)^{n_2}$, where $i = \sqrt{-1}$ is a 
Question 5 :
Find all complex numbers satisfying the equation $2|z|^2 + z^2 - 5 + i \sqrt{3} = 0$
