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Question: The complex number i +\(\sqrt{3}\) in polar form can be written as :...

The complex number i +3\sqrt{3} in polar form can be written as :

A

12(sin⁡π6+icos⁡π6)\frac{1}{\sqrt{2}}\left( \sin\frac{\pi}{6} + i\cos\frac{\pi}{6} \right)

B

2(cos⁡π6+isin⁡π6)2\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)

C

12(sin⁡π6+icos⁡π6)\frac{1}{2}\left( \sin\frac{\pi}{6} + i\cos\frac{\pi}{6} \right)

D

4(cos⁡π6+isin⁡π6)4\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)

Answer

2(cos⁡π6+isin⁡π6)2\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)

Explanation

Solution

Sol. If i +3\sqrt{3} = 2(32+i2)=2(cos⁡π6+isin⁡π6)\left( \frac{\sqrt{3}}{2} + \frac{i}{2} \right) = 2\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)