Question

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

Complex numbers
ANSWERED
asked 2021-01-24

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

 

Expert Answers (1)

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 \(\sqrt{3+i}\)

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