JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z\) and \(w\) are two complex numbers such that \(|zw| = 1\) and \(arg(z) -arg(w) =\frac {\pi }{2},\) then
- A \(\bar zw\,\, = \,i\)
- B \(z\bar w\,\, = \,\frac{{ - 1 + i}}{{\sqrt 2 }}\)
- C \(z\bar w\,\, = \,\frac{{1 - i}}{{\sqrt 2 }}\)
- D \(\bar zw\,\, = - \,i\)
Answer & Solution
Correct Answer
(D) \(\bar zw\,\, = - \,i\)
Step-by-step Solution
Detailed explanation
\(|z| \cdot|w|=1 \quad z =\) \(r e^{\left(\theta+\frac{\pi}{2}\right)} \text { and } w\) \(=\frac{1}{r} e^{i \theta}\) \(\bar{z} \cdot w\) \(=e^{-i\left(\theta+\frac{\pi}{2}\right)} \cdot e^{i \theta} \) \(=e^{-i\left(\frac{\pi}{2}\right)}=-i\)…
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