If |z - 3 + 2i| leq 4,then the difference bet | vedclass

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

Question

(B) The given equation $|z - (3 - 2i)| \leq 4$ represents a disk with center $C(3, -2)$ and radius $R = 4$.$|z|$ represents the distance of a point $z

Vedclass · Accepted Answer

$2\sqrt{13}$

Vedclass · Answer

(B) The given equation $|z - (3 - 2i)| \leq 4$ represents a disk with center $C(3, -2)$ and radius $R = 4$.$|z|$ represents the distance of a point $z$ from the origin $O(0, 0)$.The greatest and least distances from the origin to the circle occur along the line passing through the origin and the center $C$.Let $OC$ be the distance from the origin to the center $C(3, -2)$.$OC = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13}$.The least distance of $|z|$ from the origin is $|OC - R| = |\sqrt{13} - 4|$. Since $\sqrt{13} The greatest distance of $|z|$ from the origin is $OC + R = \sqrt{13} + 4$.The difference between the greatest and least values is $(4 + \sqrt{13}) - (4 - \sqrt{13}) = 2\sqrt{13}$.

If $|z - 3 + 2i| \leq 4$,then the difference between the greatest value and the least value of $|z|$ is

Similar Questions

If $\omega$ is a complex cube root of unity whose imaginary part is positive and $|z - \omega| = |z + \omega|$,then $arg(z)$ can be-

If the imaginary part of $\frac{2 z+1}{i z+1}$ is $-2$,then the locus of the point representing $z$ in the complex plane is

The locus of a point on the Argand plane represented by the complex number $z$, when $z$ satisfies the condition $\left|\frac{z-1+i}{z+1-i}\right|=\left|\operatorname{Re}\left(\frac{z-1+i}{z+1-i}\right)\right|$ is

The locus of $z$ which lies in the shaded region is best represented by

If $|z - 3i| \le 5$,then the minimum value of $|z + 2|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module