Z is a complex number such that |Z| leq 2 and | vedclass

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(C) Given $|Z| \leq 2$ and $-\frac{\pi}{3} \leq \operatorname{amp} Z \leq \frac{\pi}{3}$.This represents a sector of a circle with radius $r = 2$ unit

Vedclass · Accepted Answer

$\frac{4 \pi}{3}$

Vedclass · Answer

(C) Given $|Z| \leq 2$ and $-\frac{\pi}{3} \leq \operatorname{amp} Z \leq \frac{\pi}{3}$.This represents a sector of a circle with radius $r = 2$ units and a central angle $	heta = \frac{\pi}{3} - (-\frac{\pi}{3}) = \frac{2 \pi}{3}$.From the diagram,the locus of $Z$ forms a sector $OAB$.The area of the sector is given by the formula $A = \frac{1}{2} r^2 	heta$.Substituting the values,we get:$A = \frac{1}{2} 	imes (2)^2 	imes \frac{2 \pi}{3}$$A = \frac{1}{2} 	imes 4 	imes \frac{2 \pi}{3}$$A = \frac{4 \pi}{3} 	ext{ sq. units}$.

$Z$ is a complex number such that $|Z| \leq 2$ and $-\frac{\pi}{3} \leq \operatorname{amp} Z \leq \frac{\pi}{3}$. The area of the region formed by the locus of $Z$ is (in sq. units)

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