Express the following complex numbers in the form $z=r{{e}^{\mathrm{i}\theta }}$, where \(r\g

Question

Express the following complex numbers in the form $z=r{{e}^{\mathrm{i}\theta }}$, where $r\ge 0$ and $-\pi <\theta \le \pi $, $\frac{\cos \theta +\mathrm{i}\sin \theta }{\cos \theta -\mathrm{i}\sin \theta }$ ${{e}^{2+\mathrm{i}\theta }}$ $\frac{1}{1+{{e}^{\mathrm{i}\theta }}}$ $1+\cos \left( 2\theta \right)-\mathrm{i sin}\left( 2\theta \right)$

Accepted Answer

$e^{i2\theta}$; $e^2 e^{i\theta}$; $\frac{1}{2}\sec\frac{\theta}{2} \cdot e^{-i\frac{\theta}{2}}$; $2\cos\theta \cdot e^{-i\theta}$

Expressing Various Complex Numbers in Exponential Form

Expressing Various Complex Numbers in Exponential Form

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