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Q.
For all complex numbers z of the form 1 + i$\alpha$, $\alpha$ $\epsilon$ R, if z2 = x + iy, then :
JEE MainJEE Main 2014Complex Numbers and Quadratic Equations
Solution:
$(1+i \alpha)^{2}=x+i y$
$1-\alpha^{2}+2 i \alpha= x + i y$
so $x=1-\alpha^{2}, y=2 \alpha$
putting $ \alpha= y / 2$
$x=1-\left(\frac{y}{2}\right)^{2} $
$\Rightarrow y^{2}+4 x-4=0$