Let z_1 and z_2 be two non-zero complex numbe | vedclass

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(A) The argument of a product of complex numbers is given by $\arg(z_1 z_2) = \arg z_1 + \arg z_2 + 2k\pi$, where $k \in \{0, 1, -1\}$.Since the princ

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Principal value of $\arg(z_1 z_2)$ may not be equal to Principal value of $\arg z_1 +$ Principal value of $\arg z_2$

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(A) The argument of a product of complex numbers is given by $\arg(z_1 z_2) = \arg z_1 + \arg z_2 + 2k\pi$, where $k \in \{0, 1, -1\}$.Since the principal value of the argument lies in the interval $(-\pi, \pi]$, the sum of the principal arguments may fall outside this range.Therefore, the principal value of $\arg(z_1 z_2)$ is not necessarily equal to the sum of the principal values of $\arg z_1$ and $\arg z_2$.Similarly, for the quotient, $\arg(z_1 / z_2) = \arg z_1 - \arg z_2 + 2k\pi$, which also may not equal the difference of the principal values.

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 non-zero complex numbers. Then

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