mfausantosngcl

2023-02-24

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

Troy Jimenez

Beginner2023-02-25Added 3 answers

As you are aware (I suppose they are in degrees):

$\mathrm{cos}30\xb0=\frac{\sqrt{3}}{2}$

$\mathrm{sin}30\xb0=\frac{1}{2}$

Hence:

$z=8(\mathrm{cos}30\xb0+i\mathrm{sin}30\xb0)=8\left(\frac{\sqrt{3}}{2}\right)+i8\left(\frac{1}{2}\right)=$

$=4\sqrt{3}+4i$

in the form: $a+ib$

$\mathrm{cos}30\xb0=\frac{\sqrt{3}}{2}$

$\mathrm{sin}30\xb0=\frac{1}{2}$

Hence:

$z=8(\mathrm{cos}30\xb0+i\mathrm{sin}30\xb0)=8\left(\frac{\sqrt{3}}{2}\right)+i8\left(\frac{1}{2}\right)=$

$=4\sqrt{3}+4i$

in the form: $a+ib$