Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: Level 1

If $z=i \left(i+\sqrt{2}\right)$, then the value of $z^4+4z^3+6z^2+4z$ is

If ${\left(x+iy\right)}^2=7+24i,$ then the value of ${\left(7+\sqrt{-576}\right)}^{\frac{1}{2}}-{\left(7-\sqrt{-576}\right)}^{\frac{1}{2}}$ is

If $\left|z\right|=1,$then the value of ${\left|z-2\right|}^2+{\left|\frac{1}{z}+2\right|}^2$ is 

If $\left|z_1\right|=\left|z_2\right|$ and $\arg \left(\frac{z_1}{z_2}\right)=\pi$, then $z_1+z_2$ is equal to

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1-2z_2}{2-z_1{\overline{z}}_2}\right|=1$ and $\left|z_2\right|\ne 1$, find $\left|z_1\right|$.

The sum of ${162}^{th}$ power of the roots of the equation $x^3-2x^2+2x-1=0$ is ______.

If a complex number $z$ lies on a circle of radius $3$ and centre at $z_0=0$ then the complex number $\left(-3+9z\right)$ lies on a circle of radius

If $z_1, z_2, z_3$ are vertices of an equilateral triangle with orthocentre $z_0$ then $z_1^2+z_2^2+z_3^2=k{z}_0^2$, where $k\in N$, then $k$ is equal to