If $|z-2+i| \leq 2$,then the difference between the greatest and least value of $|z|$ is $(i=\sqrt{-1})$.

The locus of the complex number $Z$ such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is

If $w = \frac{z}{z - \frac{1}{3}i}$ and $|w| = 1$,where $i = \sqrt{-1}$,then $z$ lies on

Let $z$ and $w$ be two non-zero complex numbers such that $|z| = |w|$ and $arg(z) + arg(w) = \pi$. Then $z$ is equal to:

Let $z$ be a complex number such that $|z + 2| = |z - 2|$ and $\arg\left(\frac{z + 3}{z - i}\right) = \frac{\pi}{4}$. Then $|z|^2$ is equal to:

If the point $P$ denotes the complex number $z=x+iy$ in the Argand plane and $\frac{z-(2-i)}{z+(1+2i)}$ is a purely imaginary number,then the locus of $P$ is