Mathematics | VITEEE 2018 | Discussion Page

1)

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

A)

$\frac{\pi}{6}$

B)

$\frac{\pi}{4}$

C)

$\frac{\pi}{3}$

D)

$\frac{\pi}{2}$

Option C

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

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