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