Q42 / 120 · VITEEE 2018 · Mathematics

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

  • A
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{4}$
  • Correct answer
    C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{2}$

Solution

$\operatorname{Let} r(\cos \theta+i \sin \theta)$ $=\frac{1+i \sqrt{3}}{\sqrt{3}+1}=\frac{1}{\sqrt{3}+1}+i \frac{\sqrt{3}}{\sqrt{3}+1}$ $\Rightarrow r \cos \theta=\frac{1}{\sqrt{3}+1} ; r \sin \theta=\frac{\sqrt{3}}{\sqrt{3}+1}$

Hence, the correct answer is option: 'C'.

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