JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q28

MathematicsInteger+4 / -1Question 28 of 90

Sum of squares of modulus of all the complex numbers $z$ satisfying $\bar z=iz^2+z^2-z$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 2

Rewrite. $z+\bar z=(1+i)z^2$ . With $z=x+iy$ : $x^2-y^2+2xy=0$ and $x^2-y^2-2xy=2x$ .

Solutions. Subtracting, $x=0$ (giving $z=0$ ) or $y=-\frac12$ with $x^2-x-\frac14=0$ .

Sum of $|z|^2$ . $x_1^2+x_2^2+\frac12=1+\frac12+\frac12=2$ .

Answer: 2

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 28