For all complex numbers z of the form 1 + iα, α ϵ R, if z2 = x + iy, then :

Question

For all complex numbers z of the form 1 + iα, α ϵ R, if z2 = x + iy, then : (A) y2 - 4x + 2 = 0 (B) y2 + 4x - 4 = 0 (C) y2 - 4x + 4 = 0 (D) y2 + 4x + 2 = 0

Tardigrade Admin · Accepted Answer

(1+i α)2=x+i y 1-α2+2 i α= x + i y so x=1-α2, y=2 α putting α= y / 2 x=1-((y/2))2 ⇒ y2+4 x-4=0

Q. For all complex numbers z of the form 1 + i $α$ , $α$ $ϵ$ R, if z² = x + iy, then :

$y^{2} - 4 x + 2 = 0$

$y^{2} + 4 x - 4 = 0$

$y^{2} - 4 x + 4 = 0$

$y^{2} + 4 x + 2 = 0$

$(1 + i α)^{2} = x + i y$
$1 - α^{2} + 2 i α = x + i y$
so $x = 1 - α^{2}, y = 2 α$
putting $α = y /2$
$x = 1 - (\frac{y}{2})^{2}$
$\Rightarrow y^{2} + 4 x - 4 = 0$

Q. For all complex numbers z of the form 1 + iα, α ϵ R, if z2 = x + iy, then :

y2−4x+2=0

y2+4x−4=0

y2−4x+4=0

y2+4x+2=0