Question

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

• A. $\frac{1}{\sqrt{2}}\left( \sin\frac{\pi}{6} + i\cos\frac{\pi}{6} \right)$
• B. 2$\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)$
• C. $\frac{1}{2}\left( \sin\frac{\pi}{6} + i\cos\frac{\pi}{6} \right)$
• D. 4$\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)$

Answer 1

Answer: (B)

2$\left( \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)$

Answer 2

Sol. i + $\sqrt{3}$ = 2 $\left( \frac{\sqrt{3}}{2} + \frac{i}{2} \right)$ = 2 $\left( 1 + 1\frac{2x}{2\sqrt{1 + x^{2}}} \right)$