If $z$ is a complex number such that $|z| = 4$ and $\text{arg}(z) = \frac{5\pi}{6}$,then $z$ is equal to

If the amplitude of $(z-1-2i)$ is $\frac{\pi}{3}$,then the locus of $z$ is

Let $z_0$ be a root of the quadratic equation,$x^2 + x + 1 = 0$. If $z = 3 + 6iz_0^{81} - 3iz_0^{93}$,then $\arg(z)$ is equal to

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} - i}$ 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 the two values of $z = \sqrt{\frac{1-i}{1+i}}$ be $z_1$ and $z_2$. If $-\frac{\pi}{2} < \operatorname{Arg}(z_1) < \operatorname{Arg}(z_2) < \pi$,then $\arg(z_1) + \arg(z_2) = $