If z_1, z_2, z_3 in mathbb{C} such that |z_1| | vedclass

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

Question

(B) Let $|z_1| = |z_2| = |z_3| = R = 2$. Let $a = |z_1 - z_2|$,$b = |z_2 - z_3|$,and $c = |z_3 - z_1|$. We know that for any complex numbers $z_1, z_2

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) Let $|z_1| = |z_2| = |z_3| = R = 2$. Let $a = |z_1 - z_2|$,$b = |z_2 - z_3|$,and $c = |z_3 - z_1|$. We know that for any complex numbers $z_1, z_2, z_3$ on a circle of radius $R$,the expression $ab + bc + ca$ is maximized when the points form an equilateral triangle inscribed in the circle. For an equilateral triangle inscribed in a circle of radius $R$,the side length is $s = R\sqrt{3}$. Here,$R = 2$,so $s = 2\sqrt{3}$. Then $a = b = c = 2\sqrt{3}$. The expression becomes $a^2 + a^2 + a^2 = 3a^2$. Substituting $a = 2\sqrt{3}$,we get $3(2\sqrt{3})^2 = 3(4 	imes 3) = 3(12) = 36$. Thus,the greatest value is $36$.

If $z_1, z_2, z_3 \in \mathbb{C}$ such that $|z_1| = |z_2| = |z_3| = 2$,then the greatest value of the expression $|z_1 - z_2||z_2 - z_3| + |z_2 - z_3||z_3 - z_1| + |z_3 - z_1||z_1 - z_2|$ is

Similar Questions

Given $z$ is a complex number such that $|z| < 2$,then the maximum value of $|iz + 6 - 8i|$ is equal to-

If $|z_1+z_2|^2=|z_1|^2+|z_2|^2$,where $z_1$ and $z_2$ are two complex numbers,then

The polar coordinates of the point,whose Cartesian coordinates are $(-2 \sqrt{3}, 2)$,are

The locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$,is

If the four points $A, B, C, D$ in the Argand plane represented respectively by the complex numbers $2+i, 4+3i, 2+5i, 3i$ lie on a circle,then the centre of the circle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module