(Solved): Write the following numbers in the polar form \( r e^{i \theta},-\pi ...

Write the following numbers in the polar form \( r e^{i \theta},-\pi<\theta \leq \pi \) : (a) \( \pi i \) \[ r=\quad, \theta=\frac{\pi}{2} \] (b) \( -2 \sqrt{3}-4 i \) \[ r=\quad, \theta= \] (c) \( (1-i)(-\sqrt{2}+i) \) \[ r=\quad, \theta= \] (d) \( (\sqrt{3}-2 i)^{2} \) \[ r=, \theta= \] (e) \( \frac{-3+\sqrt{3} i}{5+4 i} \) \[ r=\quad, \theta=\quad, \] (f) \( \frac{-\sqrt{7}(1+i)}{\sqrt{3}+i} \) \[ r=\quad, \theta= \]