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STD 11 - 4.1 complex nubers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.1 complex nubers1 Mark
MCQ
If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to
  • ✓
    $\pi $
  • B
    $ - \pi $
  • C
    $ - \frac{\pi }{2}$
  • D
    $\frac{\pi }{2}$
✓

Answer

Correct option: A.
$\pi $
a
(a) Since arg $z < 0$ i.e. -ve, we choose $arg\ z = -\theta$
where $\theta $ is $+ve$
$arg\  ( - z) = - [ + \pi - ( - \theta )]$
$ = - \pi - \theta = 2\pi + ( - \pi - \theta ) = \pi + arg(z)$
$ \Rightarrow \,arg\,( - z) - arg(z) = \pi .$

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