Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: WBJEE 2018

The general value of the real angle $\theta ,$ which satisfies the equation, $(\cos \theta +i\sin \theta )(\cos 2\theta +i\sin 2\theta )\dots (\cos n\theta +i\sin n\theta )=1$ is given by, (assuming $k$ is an integer)

If $\theta \in \mathrm{ℝ}$ and $\frac{1-i\cos \theta }{1+2i\cos \theta }$ is real number, then $\theta$ will be (when $I:$ Set of integers)

If $Z_r=\sin \frac{2\pi r}{11}-i\cos \frac{2\pi r}{11},$ then $\sum _{r=0}^{10}{Z}_r$ is equal to

For any non-zero complex number $z,$ the minimum value of $\left|z\right|+|z-1|$ is

Let $z_1$ and $z_2$ be complex numbers such that $z_1\ne z_2$ and $\left|z_1\right|=\left|z_2\right|.$ If $Re\left(z_1\right)>0$ and $Im\left(z_2\right)<0,$ then $\frac{z_1+z_2}{z_1-z_2}$ is

The number of complex numbers $p$ such the $\left|p\right|=1$ and imaginary part of $p^4$ is $0,$ is

The equation $z\overline{z}+(2-3i)z+(2+3i)\overline{z}+4=0$ represents a circle of radius

If $z_1$ and $z_2$ be two non-zero complex numbers such that $\frac{z_1}{z_2}+\frac{z_2}{z_1}=1,$ then the origin and the points represented by $z_1$ and $z_2$