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(C) The principal argument of a complex number $z$ lies in the interval $(-\pi, \pi]$.Given that $\alpha$ and $\beta$ are the principal arguments of $

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$\alpha + \beta - 2\pi$

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(C) The principal argument of a complex number $z$ lies in the interval $(-\pi, \pi]$.Given that $\alpha$ and $\beta$ are the principal arguments of $z_1$ and $z_2$ respectively,the argument of the product $z_1 z_2$ is $	ext{arg}(z_1 z_2) = \alpha + \beta$.Since $-\pi We are given the condition $\alpha + \beta > \pi$.To bring the argument back into the principal range $(-\pi, \pi]$,we subtract $2\pi$ from the sum.Thus,the principal argument of $z_1 z_2$ is $\alpha + \beta - 2\pi$.

List-$I$ (Complex number)	List-$II$ (Polar form)
$(i) \sqrt{3}-i$	$(a) 2 \operatorname{cis} \frac{\pi}{6}$
$(ii) \sqrt{3}+i$	$(b) 2 \operatorname{cis} \frac{5 \pi}{6}$
$(iii) -\sqrt{3}+i$	$(c) 2 \operatorname{cis}\left(-\frac{5 \pi}{6}\right)$
$(iv) -\sqrt{3}-i$	$(d) 2 \operatorname{cis}\left(-\frac{\pi}{6}\right)$

Let $z_1$ and $z_2$ be two complex numbers with $\alpha$ and $\beta$ as their principal arguments such that $\alpha + \beta > \pi$,then the principal argument of $z_1 z_2$ is given by:

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