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  4. Arg z + Arg bar z. ( z ≠ 0) is

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Q. Arg z + Arg $ \bar z. ( z \neq 0)$ is

Complex Numbers and Quadratic Equations

Solution:

Let $z=re^{i\theta} \therefore \bar{z}=re^{-i\theta}\bigg]$
$\Rightarrow Arg, z+Arg. \bar{z}=\theta-\theta=0$.
$[\because -\pi < \theta \le \pi$ for $Arg \,2]$