If $|z| = 4$ and $\text{arg}(z) = \frac{5\pi}{6}$,then $z =$

If $Z_1$ and $Z_2$ are complex numbers such that $|Z_1+Z_2|=|Z_1|+|Z_2|$,then the difference in the amplitudes of $Z_1$ and $Z_2$ is

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$ then $\text{arg}({z_1}) - \text{arg}({z_2})$ is equal to

Let $z_1$ and $z_2$ be two complex numbers with $\alpha$ and $\beta$ as their principal arguments such that $\alpha + \beta > \pi$,then the principal argument of $z_1 z_2$ is given by:

If $z_1, z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers,then $\arg \left( \frac{z_1}{z_4} \right) + \arg \left( \frac{z_2}{z_3} \right)$ equals

If $z_1 = 5 - 2i$ and $z_2 = 3 + i$,where $i = \sqrt{-1}$,then $\arg \left(\frac{z_1 + z_2}{z_1 - z_2}\right)$ is