Embibe Experts Solutions for Exercise 3: Assignment

If $z_1,z_2$ and $z_3,z_4$ are two pairs of conjugate complex numbers, then $\arg \left(\frac{z_1}{z_3}\right)+\arg \left(\frac{z_2}{z_4}\right)$ is

If $\arg z=\frac{\pi }{4}$, then

The argument of $-2+2\sqrt{3}i$ is

The polar form of complex number $\sqrt{3}+i$ is

If $z=\frac{1+3i}{1-i}$, then (where $i=\sqrt{-1}$)

The argument of $-3i·|5-13i|$ is

Let $z=3+xi$ where $x$ is a non-zero real number and $i=\sqrt{-1}$. If the imaginary part of $z^2$ is equal to imaginary part of $z^3$ then $x^2$ is equal to

If $x=3+4i$ then the value of $204x-70x^2+12x^3-x^4$ is