The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are

Modulus of $\left( {\frac{{3 + 2i}}{{3 - 2i}}} \right)$ is

The inequality $|z - 4|\, < \,|\,z - 2|$represents the region given by

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

If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is

If $z $ is a complex number of unit modulus and  argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.