If $z = x + iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5 i|=0$, then

If $z_1 = 1+2i$ and $z_2 = 3+5i$ , then ${\mathop{\rm Re}\nolimits} \,\left( {\frac{{{{\overline Z }_2}{Z_1}}}{{{Z_2}}}} \right) = $

Let $z$ =${i^{2i}}$ , then $|z|$ is (where $i$ =$\sqrt { - 1}$ )

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

If $z$ and $\omega$ are two complex numbers such that $|z \omega|=1$ and $\arg (z)-\arg (\omega)=\frac{3 \pi}{2}$, then $\arg \left(\frac{1-2 \bar{z} \omega}{1+3 \bar{z} \omega}\right)$ is:

(Here arg(z) denotes the principal argument of complex number $z$ )

Let $Z$ and $W$ be complex numbers such that $\left| Z \right| = \left| W \right|,$ and arg $Z$ denotes the principal argument of $Z.$

Statement $1:$ If arg $Z+$ arg $W = \pi ,$ then $Z = -\overline W $.

Statement $2:$ $\left| Z \right| = \left| W \right|,$ implies arg $Z-$ arg $\overline W = \pi .$