Discussion Forum



1)

Amplitude of $\frac{1+\sqrt{3i}}{\sqrt{3}+1}$ is :


A) $\frac{\pi}{6}$

B) $\frac{\pi}{4}$

C) $\frac{\pi}{3}$

D) $\frac{\pi}{2}$

Answer:

Option C

Explanation:

Let r(cos θ + isin θ) = $\frac{1+i\sqrt{3}}{\sqrt{3}+1}$

=$\frac{1}{\sqrt{3}+1}+i\frac{\sqrt{3}}{\sqrt{3}+1}$

 r cos θ = $\frac{1}{\sqrt{3}+1}$ ; r sin θ = $\frac{\sqrt{3}}{\sqrt{3}+1}$

→ tan θ = √3 

→ θ = $\frac{\pi}{3}$