Q112 / 155 · WBJEE 2022 · Mathematics

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

  • Correct answer
    A
    Principal value of $\arg \left(z_1 z_2\right)$ may not be equal to Principal value of arg $z_1+$ Principal value of arg $z_2$
  • B
    Principal value of $\arg \left(z_1 z_2\right)=$ Principal value of $\arg z_1+$ Principal value of $\arg z_2$
  • C
    Principal value of $\arg \left(z_1 / z_2\right)=$ Principal value of $\arg z_1-$ Principal value of $\operatorname{argz} z_2$
  • Correct answer
    D
    Principal value of $\arg \left(z_1 / z_2\right)$ may not be $\arg z_1-\arg z_2$

Solution

$\arg \left(z_1 z_2\right)=\operatorname{argz_{1}}+\operatorname{argz_{2}}+2 k \pi$ $\arg \left(z_1 / z_2\right)=\operatorname{argz_{1}}-\operatorname{argz_{2}}+2 \mathrm{k} \pi$

Hence, the correct answer is options: 'A', 'D'.

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