Let ${z_1}$ be a complex number with $|{z_1}| = 1$ and ${z_2}$ be any complex number,then $\left| \frac{{z_1 - z_2}}{{1 - z_1 \bar{z}_2}} \right| = $

The argument and modulus of $\frac{1 + i}{1 - i}$ are respectively:

If $|a_k| < 1, \lambda_k \ge 0$ for $k = 1, 2, ..., n$ and $\lambda_1 + \lambda_2 + ... + \lambda_n = 1$,then the value of $|\lambda_1 a_1 + \lambda_2 a_2 + ... + \lambda_n a_n|$ is

If $z \neq 0$ is a complex number such that $|z - \frac{1}{z}| = 2$,then the maximum value of $|z|$ is:

Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2$ and $z_1 z_2$ are both real. Then:

If $z$ is a complex number such that $\left|z-\frac{4}{z}\right|=2$,then the greatest value of $|z|$ is