Question

# Write each complex number in standard form.2(cos 30^@ + i sin 30^@)

Complex numbers

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

2021-01-25

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