JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q3

← JEE Main 2022 · 27 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 3 of 90

Let the minimum value $v_0$ of $v=|z|^2+|z-3|^2+|z-6i|^2$ , $z\in\mathbf C$ is attained at $z=z_0$ . Then $\left|2z_0^2-\bar z_0^3+3\right|^2+v_0^2$ is equal to

1000

1024

1105

1196

Answer and worked solution

Official answer: A

Minimum at the centroid of $0$ , $3$ , $6i$ : $z_0=1+2i$ , and $v_0=5+8+17=30$ .

Compute. $2z_0^2=-6+8i$ and $\bar z_0^3=(1-2i)^3=-11+2i$ , so $2z_0^2-\bar z_0^3+3=8+6i$ , with $|\cdot|^2=100$ .

$100+900=1000$ . (A)

Topics:Geometry in the complex plane Algebra of complex numbers

← Previous question Next question →

JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 3