mfausantosngcl

2023-02-24

Write the complex number $8\left(\mathrm{cos}30+i\mathrm{sin}30\right)$ in standard form?

Troy Jimenez

As you are aware (I suppose they are in degrees):
$\mathrm{cos}30°=\frac{\sqrt{3}}{2}$
$\mathrm{sin}30°=\frac{1}{2}$
Hence:
$z=8\left(\mathrm{cos}30°+i\mathrm{sin}30°\right)=8\left(\frac{\sqrt{3}}{2}\right)+i8\left(\frac{1}{2}\right)=$
$=4\sqrt{3}+4i$
in the form: $a+ib$

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