JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q30

← JEE Main 2022 · 27 Jul · Shift 1

MathematicsInteger+4 / -1Question 30 of 90

Let $S=\left\{z\in\mathbf C:z^2+\bar z=0\right\}$ . Then $\displaystyle\sum_{z\in S}\left(\operatorname{Re}(z)+\operatorname{Im}(z)\right)$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 0

Real and imaginary parts. $x^2-y^2+x=0$ and $y(2x-1)=0$ .

Solutions. $z=0,-1,\frac12\pm\frac{\sqrt3}2i$ .

Sum of $\operatorname{Re}+\operatorname{Im}$ $=0-1+1=0$ .

Answer: 0

Topics:Algebra of complex numbers

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 30