Argument of - 1 - i 3 is - Vidyadip

MCQ

Argument of $ - 1 - i\sqrt 3 $ is

A
$\frac{{2\pi }}{3}$
B
$\frac{\pi }{3}$
C
$ - \frac{\pi }{3}$
✓
$ - \frac{{2\pi }}{3}$

✓

Answer

Correct option: D.

$ - \frac{{2\pi }}{3}$

d
(d) Let $z = - 1 - i\sqrt 3 $
then $\alpha = {\tan ^{ - 1}}\left| {\,\frac{b}{a}\,} \right| = {\tan ^{ - 1}}\left| {\, - \frac{{\sqrt 3 }}{1}\,} \right| = \frac{\pi }{3}$
Clearly, $z$ is in $III$ quadrant.
Therefore argument $\theta = - (\pi - \alpha ) = - (\pi - \pi /3) = \frac{{ - 2\pi }}{3}$.

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