Jaylene Franco

2022-01-30

How do you write the complex number in standard form $\left[3\left(\mathrm{cos}\left(\frac{\pi }{3}\right)+i\mathrm{sin}\left(\frac{\pi }{3}\right)\right)\right]\left[4\left(\mathrm{cos}\left(\frac{\pi }{6}\right)+i\mathrm{sin}\left(\frac{\pi }{6}\right)\right)\right]$?

Frauental91

Use ${e}^{i\theta }=\mathrm{cos}\theta +i\mathrm{sin}\theta$
$=12{e}^{i\left(\left(\frac{1}{3}+\frac{1}{6}\right)\pi \right)}$
$=12{e}^{i\frac{\pi }{2}}$
$=12\left(\mathrm{cos}\left(\frac{\pi }{2}\right)+i\mathrm{sin}\left(\frac{\pi }{2}\right)\right)$
$i12$

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