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

Given $z$ is a complex number such that  $|z| < 2,$ then the maximum value of $|iz + 6 -8i|$ is equal to-

The values of $z$for which $|z + i|\, = \,|z - i|$ are

Let $z$ be a complex number (not lying on $X$-axis) of maximum modulus such that $\left| {z + \frac{1}{z}} \right| = 1$. Then

Find the modulus and the argument of the complex number $z=-1-i \sqrt{3}$.

If ${z_1}$ and ${z_2}$ are two complex numbers, then $|{z_1} - {z_2}|$ is