Embibe Experts Solutions for Chapter: Complex Numbers and Quadratic Equations, Exercise 1: Exercise

The value of $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1$ is

A real value of $x$ satisfies the equation $\frac{3-4ix}{3+4ix}=a-ib(a,b\in R),\text{ if }{a}^2+b^2=$

The value of $(1+i{)}^4+(1-i{)}^4$ is

Which of the following is correct for any two complex numbers $z_1$ and $z_2$?

The complex number $z$ which satisfy the equation $\left|\frac{i+z}{i-z}\right|=1$ lies on

If $f\left(z\right)=\frac{7-z}{1-z^2}$, where $z=1+2i$, then $\left|f\left(z\right)\right|=$

If $z$ is a complex number, then

If $z=a+ib$ lies in the third quadrant, then $\frac{\overline{z}}{z}$ also lies in the third quadrant if