Expressing Various Complex Numbers in Exponential Form
Express the following complex numbers in the form $z=r{{e}^{\text{i}\theta }}$, where $r\ge 0$ and $-\pi <\theta \le \pi $,
(i)
$\frac{\cos \theta +\text{i}\sin \theta }{\cos \theta -\text{i}\sin \theta }$
(ii)
${{e}^{2+\text{i}\theta }}$
(iii)
$\frac{1}{1+{{e}^{\text{i}\theta }}}$
(iv)
$1+\cos \left( 2\theta \right)-\text{i sin}\left( 2\theta \right)$
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