Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: AMU-AT (B.Tech.) 2018

A real value of $x$ will satisfy the equation $\left(\frac{3-4ix}{3+4ix}\right)=\alpha -i\beta$ $(\alpha , \beta$ are real$),$ if

If $\omega$ is a complex cube root of unity, then the value of $\frac{p+q\omega +r{\omega }^2}{r+p\omega +q{\omega }^2}+\frac{p+q\omega +r{\omega }^2}{q+r\omega +p{\omega }^2}, \left(p,q,r\in R\right)$  is equal to

If $n$ is a positive integer, then ${\left(1+i\right)}^n+\left(1-i\right){}^n$ is equal to

The amplitude of the complex number $1+\sin \alpha -i\cos \alpha$ is

The points $z_i=x+iy$ and $z_2=\frac{1}{-x+iy}$ in the complex plane lie on