JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z _{1}\) and \(z _{2}\) be two complex numbers such that \(\overline{ z }_{1}=i \overline{ z }_{2}\) and \(\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi\). Then
- A \(\arg z _{2}=\frac{\pi}{4}\)
- B \(\arg z _{2}=-\frac{3 \pi}{4}\)
- C \(\arg z _{1}=\frac{\pi}{4}\)
- D \(\arg z _{1}=-\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\arg z _{1}=\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\overline{ z }_{1}= i _{2}\) \(z _{1}=- iz _{2}\) \(\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi\) \(\arg \left(- i \frac{ z _{2}}{\overline{ z }_{2}}\right)=\pi \quad \arg \left( z _{2}\right)=\theta\) \(-\frac{\pi}{2}+\theta+\theta=\pi\)…
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