AP EAMCET · Maths · Complex Number
Let \(z\) and \(w\) be two distinct non-zero complex numbers if \(|z|^2 w-|w|^2 z=z-w\), then
- A \(w=\bar{z}^2\)
- B \(z \bar{W}=2\)
- C \(z \bar{W}=1\)
- D \(W=\bar{Z}\)
Answer & Solution
Correct Answer
(C) \(z \bar{W}=1\)
Step-by-step Solution
Detailed explanation
\begin{array}{ll} & \left(|z|^2+1\right) w=\left(|w|^2+1\right) z \\ \therefore & \text { Let } z=k w, k \neq 1, k \neq 0 \\ \therefore & k^2|w|^2 w-k|w|^2 w=k w-w \\ \therefore & k|w|^2 w(k-1)=(k-1) w \\ \Rightarrow & k=\frac{1}{|w|^2} \\ \therefore & z=\frac{w}{|w|^2} \\ &…
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