If Z is a complex number such that |Z| leq 3 | vedclass

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(B) Given conditions are $|Z| \leq 3$ and $-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$.$|Z| \leq 3$ represents a disk of radius $3$

Vedclass · Accepted Answer

$\frac{9 \pi}{2}$

Vedclass · Answer

(B) Given conditions are $|Z| \leq 3$ and $-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$.$|Z| \leq 3$ represents a disk of radius $3$ centered at the origin.$-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$ represents the region in the first and fourth quadrants (the right half-plane).Thus,the locus of $Z$ is a semicircle with radius $r = 3$.The area of the region is $\frac{1}{2} \pi r^2 = \frac{1}{2} 	imes \pi 	imes (3)^2 = \frac{9 \pi}{2}$.

If $Z$ is a complex number such that $|Z| \leq 3$ and $-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$,then the area of the region formed by the locus of $Z$ is

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