JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q62

MathematicsSingle correct+4 / -1Question 62 of 90

For all complex numbers $z$ of the form $1+i\alpha$ , $\alpha\in\mathbb R$ , if $z^2=x+iy$ , then :

y^2-4x+2=0

y^2+4x-4=0

y^2-4x+4=0

y^2+4x+2=0

Answer and worked solution

Official answer: B

$z^2=(1-\alpha^2)+2i\alpha$ , so $x=1-\alpha^2$ and $y=2\alpha$ . Eliminating α:
$x=1-\frac{y^2}4\iff y^2+4x-4=0.$

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 62