Kye

2021-01-24

Write each complex number in standard form. $2\left(\mathrm{cos}{30}^{\circ }+i\mathrm{sin}{30}^{\circ }\right)$

saiyansruleA

The standard form of complex number is a+ib
So, consider $2\left(\mathrm{cos}{30}^{\circ }+i\mathrm{sin}{30}^{\circ }\right)$
$=2\left(\frac{\sqrt{3}}{2}+i\frac{1}{2}\right)\left[\therefore \mathrm{cos}{30}^{\circ }=\frac{\sqrt{3}}{2}\mathrm{sin}{30}^{\circ }=\frac{1}{2}\right]$
$=2\left(\frac{\sqrt{+}i}{2}\right)$
Here $\sqrt{3+i}$ is of the form a+ib
Hence, the standard form of given complex number is $\sqrt{3+i}$

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