<p>Express the following complex numbers in the form $z=r{{e}^{\mathrm{i}\theta }}$, where $r\ge 0$ and $-\pi <\theta \le \pi $,</p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{\cos \theta +\mathrm{i}\sin \theta }{\cos \theta -\mathrm{i}\sin \theta }$</div></li><li><div class="list-item-paragraph">${{e}^{2+\mathrm{i}\theta }}$</div></li><li><div class="list-item-paragraph">$\frac{1}{1+{{e}^{\mathrm{i}\theta }}}$</div></li><li><div class="list-item-paragraph">$1+\cos \left( 2\theta \right)-\mathrm{i sin}\left( 2\theta \right)$</div></li></ol>

Express the following complex numbers in the form $z=r{{e}^{\mathrm{i}\theta }}$, where $r\ge 0$ and $-\pi <\theta \le \pi $,

$\frac{\cos \theta +\mathrm{i}\sin \theta }{\cos \theta -\mathrm{i}\sin \theta }$

$1+\cos \left( 2\theta \right)-\mathrm{i sin}\left( 2\theta \right)$

Complex Numbers - General

Complex Numbers

H2 Math

International Baccalaureate Higher Level Mathematics

Expressing Various Complex Numbers in Exponential Form

Expressing Various Complex Numbers in Exponential Form

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