Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: VITEEE 2018 Shift 1

If $z=x+iy, z^{\frac{1}{3}}=a-ib$, then $\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)$ where $k$ is equal to

If $z=\frac{7-i}{3-4i}$, then $z^{14}=$

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ is

One of the values of ${\left(\frac{1+i}{\sqrt{2}}\right)}^{\frac{2}{3}}$ is

If $\omega =\frac{-1+\sqrt{3}i}{2}$, then ${\left(3+\omega +3{\omega }^2\right)}^4$ is

The equation $z\overline{z}+\left(2-3i\right)z+\left(2+3i\right)\overline{z}+4=0$ represents a circle of radius