Answer :
Squaring both side
-i = (x + iy)2
= (x2-y2)+2ixy
x2-y2 = 0
2xy = -1
As we know all that,
(x2+y2)2 = (x2-y2)2+4x2y2
(x2+y2)2 = 0+1
(x2+y2)2 = 1
x2+y2 = 1
X2-y2 = 0 ……………………. (1)
x2+y2 = 1 ……………….(2)
From (1)
x2 = y2…………….(3)
2x2 = 1 (because x2 = y2)
2xy = -1
it means xy<0
Either x<0 , y > 0
Or x>0, y<0
X and y have different sign
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