If z= 1-i 3 1+i 3 , then (z)= - Vidyadip

MCQ

If $z=\frac{1-i \sqrt{3}}{1+i \sqrt{3}}$, then $\arg (z)=$

A
$60^{\circ}$
B
$120^{\circ}$
✓
$240^{\circ}$
D
$300^{\circ}$

✓

Answer

Correct option: C.

$240^{\circ}$

(C)
$\arg \left(\frac{1-i \sqrt{3}}{1+i \sqrt{3}}\right)=\arg (1-i \sqrt{3})-\arg (1+i \sqrt{3})$
$=-60^{\circ}-60^{\circ}=-120^{\circ}$ or $240^{\circ}$
$\ldots\left[\begin{array}{c}\because \arg (1- i \sqrt{3})=-\tan ^{-1} \sqrt{3}=-60^{\circ} \\ \text { and } \arg (1+ i \sqrt{3})=\tan ^{-1} \sqrt{3}=60^{\circ}\end{array}\right]$

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