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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The minimum value of $|2z - 1| + |3z - 2|$ is

If $z = \frac{3}{2 + \cos \theta + i \sin \theta}$,then the locus of $z$ is :-

If the area of the triangle formed by the points $z, z + iz$ and $iz$ on the complex plane is $18$,then the value of $|z|$ is

The equation $z\overline{z} + (2 - 3i)z + (2 + 3i)\overline{z} + 4 = 0$ represents a circle of radius

The set of points on the Argand plane which satisfy both $|z| \leq 4$ and $\operatorname{Arg}(z) = \frac{\pi}{3}$ represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module