AP EAMCET · Maths · Complex Number
If \(Z\) is a complex number such that \(|Z| \leq 3\) and \(\frac{-\pi}{2} \leq a m p Z \leq \frac{\pi}{2}\), then the area of the region formed by locus of \(Z\) is
- A \(9 \pi\)
- B \(\frac{9 \pi}{2}\)
- C \(3 \pi\)
- D \(\frac{9 \pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{9 \pi}{2}\)
Step-by-step Solution
Detailed explanation
\(|Z| \leq 3\), \(-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}\) Required region is semicircle with radius 3. \(\text { Required area }=\frac{\pi \times 3^2}{2}=\frac{9 \pi}{2} .\)
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