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 princi

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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.

Let $z_1$ and $z_2$ be two non-zero complex numbers. Then

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