Write each complex number in standard form. 2(cos30∘+isin30∘)

Kye

Answered question

2021-01-24

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

Answer & Explanation

saiyansruleA

Skilled2021-01-25Added 110 answers

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