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Question: The argument of \(\frac{1 + i\sqrt{3}}{\sqrt{3} + 1}\)is equal to...

The argument of 1+i33+1\frac{1 + i\sqrt{3}}{\sqrt{3} + 1}is equal to

A

π6\frac{\pi}{6}

B

π4\frac{\pi}{4}

C

π3\frac{\pi}{3}

D

None of these

Answer

π3\frac{\pi}{3}

Explanation

Solution

Sol. Since arg (x + iy) = tan–1(y/x)

we have, arg (1+i33+1)=tan⁡−1[3(3+1)/1(3+1)]\left( \frac{1 + i\sqrt{3}}{\sqrt{3} + 1} \right) = \tan^{- 1}\left\lbrack \frac{\sqrt{3}}{(\sqrt{3} + 1)}/\frac{1}{(\sqrt{3} + 1)} \right\rbrack

= tan–1(3)(\sqrt{3}) = p/3