The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are
$\sqrt 2 {\rm{ and }}\frac{\pi }{6}$
$1$ and $0$
$1$ and $\frac{\pi }{3}$
$1$ and $\frac{\pi }{4}$
If $arg\, z < 0$ then $arg\, (-z)\, -arg(z)$ is equal to
The values of $z$for which $|z + i|\, = \,|z - i|$ are
Find the complex number z satisfying the equations $\left| {\frac{{z - 12}}{{z - 8i}}} \right| = \frac{5}{3},\left| {\frac{{z - 4}}{{z - 8}}} \right| = 1$
Let $z$ =${i^{2i}}$ , then $|z|$ is (where $i$ =$\sqrt { - 1}$ )
The amplitude of the complex number $z = \sin \alpha + i(1 - \cos \alpha )$ is