AP EAMCET · Maths · Complex Number
The points \(P, Q\) denote the complex numbers \(Z_1, Z_2\) in the Argand plane. ' \(O\) ' is the origin. If \(Z_1 \bar{Z}_2+\bar{Z}_1 Z_2=0\) and \(P O Q=\theta\) then \(\sin \theta=\)
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{\sqrt{3}}{2}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(Z_1 \bar{Z}_2+\bar{Z}_1 Z_2=0 \implies 2 \text{Re}(Z_1 \bar{Z}_2)=0 \implies \text{Re}(Z_1 \bar{Z}_2)=0\) Let \(Z_1 = |Z_1|e^{i\alpha}\) and \(Z_2 = |Z_2|e^{i\beta}\). Then \(\text{Re}(|Z_1||Z_2|e^{i(\alpha-\beta)})=0\) \(|Z_1||Z_2|\cos(\alpha-\beta)=0\) Since \(P\) and \(Q\)…
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