Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: SRMJEEE (UG) 2014

If $z=\sqrt{20i-21}+\sqrt{20i+21}$ then the principal value of $\arg \left(z\right)$ can be

If $Im\left(\frac{2z+1}{iz+1}\right)=-2,$ then the locus of the point representing $z$ in the complex plane is

The principal value of $i^i$ is equal to

If the imaginary part of $\frac{2z+1}{iz+1}$ is $-4,$ then the locus of the point representing $z$ in the complex plane is

If $z=a+ib$, then $i\log \left(\frac{\overline{z}}{z}\right)$ is equal to

If $z=\frac{7-i}{3-4i},$ then $z^{14}$ equals

If $z_1,z_2$ are two non-zero complex numbers such that $\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$, then $\arg \left(z_1\right)-\arg \left(z_2\right)$ is equal to

If $\mathrm{\omega }$ is an imaginary cube root of unity, then ${\left(1+\mathrm{\omega }-{\mathrm{\omega }}^2\right)}^7$ equals