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4-1.Complex numbers
easy
Argument of $ - 1 - i\sqrt 3 $ is
A
$\frac{{2\pi }}{3}$
B
$\frac{\pi }{3}$
C
$ - \frac{\pi }{3}$
D
$ - \frac{{2\pi }}{3}$
Solution
(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 $\theta = – (\pi – \alpha ) = – (\pi – \pi /3) = \frac{{ – 2\pi }}{3}$.
Standard 11
Mathematics
