Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: KEAM 2019

If $z$ is a normal root of $\sqrt[7]{-1}$ then $z^{85}+z^{142}+z^{191}$ is.

If $z_1=5y^2-3-8ix,z_2=4y^2-16i$ and $z_1={\overline{z}}_2$ then $z=x+iy$ is equal to

The value of $(1+i{)}^5\times (1-i{)}^5$ is

The value of $(1+i{)}^8+(1-i{)}^8=$

The product of all values of $(\cos \alpha +i\sin \alpha {)}^{3/5}$ is

If $3^{49}\left(x+iy\right)={\left(\frac{3}{2}+\frac{\sqrt{3}i}{2}\right)}^{100}$ and $x=ky,$ then $k$ is

If $z=\frac{\sqrt{3}+i}{2},$ then the value of $z^{69}$ is

If $\omega$ is a complex cube root of unity and $\left(1+\omega \right){}^7=A+B\omega ,$ then $A$ and $B$ are equal to