Let $z$ be a purely imaginary number such that ${\mathop{\rm Im}\nolimits} (z) < 0$. Then $arg\,(z)$ is equal to
$\pi $
$\frac{\pi }{2}$
$0$
$ - \frac{\pi }{2}$
If $\frac{\pi }{2} < \alpha < \frac{3}{2}\pi $ , then the modulus and argument of $(1 + cos\, 2\alpha ) + i\, sin\, 2\alpha $ is respectively
Find the complex number z satisfying the equations $\left| {\frac{{z - 12}}{{z - 8i}}} \right| = \frac{5}{3},\left| {\frac{{z - 4}}{{z - 8}}} \right| = 1$
$(z + a)(\bar z + a)$, where $a$ is real, is equivalent to
$|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$ is possible if
Find the modulus and argument of the complex numbers:
$\frac{1+i}{1-i}$