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 CExplanation: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 = $\frac{\pi}{3}$
