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

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

Question

(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)

Similar Questions

The roots of the cubic equation $(z + ab)^3 = a^3$,where $a \neq 0$,represent the vertices of a triangle of sides of length:

If $z=x+iy, x, y \in R$ and the imaginary part of $\frac{\bar{z}-1}{\bar{z}-i}$ is $1$,then the locus of $z$ is

If the complex numbers $z_1, z_2, z_3$ represent the vertices of an equilateral triangle such that $|z_1| = |z_2| = |z_3|$,then $z_1 + z_2 + z_3 = $

$z_1$ and $z_2$ are two complex numbers such that $\left|z_1-z_2\right| < k$. If a complex number $z$ satisfies the condition $\left|z-z_1\right|+\left|z-z_2\right|=k$,then $z$ lies on:

For any complex number $z$,the minimum value of $|z|+|z-1|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module