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

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 $|z+\overline{z}|=|z-\overline{z}|$, then the locus of $z$ 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

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

If $1, \omega$ and ${\omega }^2$ are the cube roots of unity, then the value of $\left(1+\omega \right)\left(1+{\omega }^2\right)\left(1+{\omega }^4\right)\left(1+{\omega }^8\right)$ is

$\left(x^3-1\right)$ can be factorised as, where, $\omega$ is one of the cube roots of unity.

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

$z\overline{z}+(3-i)z+(3+i)\overline{z}+1=0$ represents a circle with