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  4. If arg (z) = θ , then arg bar(z) is equal to

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Q. If $ arg \,(z) = θ $ , then $ arg\, \bar{(z)} $ is equal to

UPSEEUPSEE 2007

Solution:

Let $z = a + ib$
$\therefore \,arg\left(z\right)=\theta=tan^{-1} \frac{b}{a}$
$\because \,\bar{z}=a-ib$
$\therefore \, arg\left(\bar{z}\right)=\phi=tan^{-1}\left(-\frac{b}{a}\right)$
$=-tan^{-1}\left(\frac{b}{a}\right)$
$=-\theta$