Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$.

If $\left|z+\frac{2}{z}\right|=2$,then the maximum value of $|z|$ is

The modulus and amplitude of $\frac{1+2i}{1-(1-i)^{2}}$ are

If $a > 0$ and $z = \frac{(1+i)^2}{a+i}, (i = \sqrt{-1})$ has magnitude $\frac{2}{\sqrt{5}}$,then $\bar{z}$ is equal to

If ${z_1}, {z_2}, {z_3}$ are complex numbers such that $|{z_1}| = |{z_2}| = |{z_3}| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$,then $|{z_1} + {z_2} + {z_3}|$ is

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