Q. 2

# Write the values of the square root of –i.

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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