WBJEE · Maths · Complex Number
Let \(z_1\) and \(z_2\) be two non-zero complex numbers. Then
- 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 \(\operatorname{argz} z_2\)
- D Principal value of \(\arg \left(z_1 / z_2\right)\) may not be \(\arg z_1-\arg z_2\)
Answer & Solution
Correct Answer
(D) Principal value of \(\arg \left(z_1 / z_2\right)\) may not be \(\arg z_1-\arg z_2\)
Step-by-step Solution
Detailed explanation
\(\arg \left(z_1 z_2\right)=\operatorname{argz_{1}}+\operatorname{argz_{2}}+2 k \pi\) \(\arg \left(z_1 / z_2\right)=\operatorname{argz_{1}}-\operatorname{argz_{2}}+2 \mathrm{k} \pi\)
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