Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: BITSAT 2017

The value of $\lambda$ for which the loci $\arg z=\frac{\pi }{6}$ and $|z-2\sqrt{3}i|=\lambda$ on the argand plane touch each other is 

If $z_1$ and ${\overline{z}}_1$ represents adjacent vertices of a regular polygon of $n$ sides and if $\frac{Im\left(z_1\right)}{Re\left(z_1\right)}=\sqrt{2}-1$, then $n$ is equal to

The $n^{\mathrm{th}}$ roots of unity are in

If $z=a+ib$ satisfies $\arg (z-1)=\arg (z+3i)$, then $(a-1):b=$

If $z_1,z_2$ and $z_3$ represent the vertices of an equilateral triangle such that $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|$ then