If arg,z < 0 then arg,( - z) - arg,(z) is equal to

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4-1.Complex numbers

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If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to

A

$\pi $

B

$ - \pi $

C

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

D

$\frac{\pi }{2}$

(IIT-2000)

Solution

(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 .$

Standard 11

Mathematics

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