pagtuboy2b

2023-03-01

How to express the complex number in rectangular form: $z=5\left(\mathrm{cos}120degrees+i\mathrm{sin}120degrees\right)$?

Karbamidjts

$\left(-\frac{5}{2},\frac{5}{2}\sqrt{3}\right)$
Explanation:
using the mathematical relations between polar and rectangular coordinates.
$•x=r\mathrm{cos}\theta$
$•y=r\mathrm{sin}\theta$
here r = 5 and $\theta ={120}^{\circ }$
Therefore: $x=5{\mathrm{cos}120}^{\circ }=5×-\frac{1}{2}=-\frac{5}{2}$
and $y=5{\mathrm{sin}120}^{\circ }=5×\frac{\sqrt{3}}{2}=\frac{5}{2}\sqrt{3}$

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