JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q3

MathematicsSingle correct+4 / -1Question 3 of 75

Let $S=\left\{z\in\mathbb C:z^2+\sqrt6\,iz-3=0\right\}$ . Then $\displaystyle\sum_{z\in S}z^8$ is equal to :

162

184

262

324

Answer and worked solution

Official answer: A

Roots.
$z=\frac{-\sqrt6\,i\pm\sqrt{-6+12}}2=\frac{\sqrt6}2(\pm1-i).$
Each has $|z|^2=3$ , and arguments $-\tfrac\pi4$ and $-\tfrac{3\pi}4$ .

Eighth powers. $z^8=3^4e^{8i\theta}$ , and $8\theta$ is a multiple of $2\pi$ for both, so each is 81.

Sum: 162.

(A)

Topics:De Moivre's theorem Roots and coefficients

JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 3