11-2 pi3 is 240° right???
the argument of (1- i √3) is
(1+ i√3)
A) 60°
B) 120°
C) 210°
D) 240°
i got the answer as 240° but the book ans says it is 60°.... 'am baffled!!
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7 Answers
30First of all if the principal argument of a complex number is \theta then -\pi < \theta \leq \pi.
Over here after rationalisation we get,
z=\frac{-1}{2}-\frac{\sqrt{3}}{2}i
\theta =\tan^{-1}\left( \frac{Im(z)}{Re(z)}\right) = \tan^{-1}\sqrt{3}=\frac{\pi }{3}
Now, since both Re(z)<0 and Im(z)<0, the complex number must lie in the third quadrant of the argand plane.
Therefore, Arg(z)= \theta -\pi =-\frac{2\pi }{3}
30Yeah it is but the principal argument lies between -pi and pi only.
