For any complex number $z$,$\bar{z} = \frac{1}{z}$ if and only if

If $z_1 = 1+2i$ and $z_2 = 3+5i$,then $\text{Re} \left( \frac{\bar{z}_2 z_1}{z_2} \right) = $

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

The modulus of $\frac{1-i}{3+i}+\frac{4i}{5}$ is

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

If $z = x + iy$ with $xy \neq 0$ satisfies the equation $z^2 + i\bar{z} = 0$,then $|z^2|$ is equal to: