JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z\) and \(\omega\) are two complex numbers such that \(|z \omega|=1\) and \(\arg (z)-\arg (\omega)=\frac{3 \pi}{2}\), then \(\arg \left(\frac{1-2 \bar{z} \omega}{1+3 \bar{z} \omega}\right)\) is: (Here arg(z) denotes the principal argument of complex number \(z\) )
- A \(\frac{3 \pi}{4}\)
- B \(-\frac{\pi}{4}\)
- C \(-\frac{3 \pi}{4}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(-\frac{3 \pi}{4}\)
Step-by-step Solution
Detailed explanation
As \(|z \omega|=1\) \(\Rightarrow|z|=r\), then \(|\omega|=\frac{1}{r}\) Let \(\arg (z)=q\) \(\therefore \arg (\omega)=\left(\theta-\frac{3 \pi}{2}\right)\) \(\text { So, } z=r e^{1 \theta}\) \(\Rightarrow \bar{z}=r e^{i(-\theta)}\)…
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