Convert the complex number $4 (cos 300^{o} + i sin 300^{o})$ in the standard form $x + i y$ .

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Solution

$4 (cos 300^{o} + i sin 300^{o})$

$= 4 (cos (360 - 60)^{o} + i sin (360 - 60)^{o})$

$= 4 (cos 60^{o} - i sin 60^{o})$

$= 4 (\frac{1}{2} - i \frac{\sqrt{3}}{2})$

$= 2 - i (2 \sqrt{3})$

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