2 mathematics Q.

1. Let a = √i, s.t. a = x+yi, x,y are real numbers,
a^2 = i => x^2 + 2xyi - y^2 = i
x^2 - y^2 = 0 -----------(1)
2xy = 1 => xy = 1/2 ----------(2)
x = y or x = -y,
When x = y, y^2 = 1/2 => y = 1/√2 or -1/√2 => x = 1/√2 or -1/√2
When x = -y, -y^2 = 1/2 (rej.)
a = √i = 1/√2 + i/√2 or -1/√2 - i/√2

2. Let b = √(-i), s.t. b = x+yi, x,y are real numbers
a^2 = -i => x^2 + 2xyi- y^2 = -i
x^2 - y^2 = 0 and xy = -1/2
x =y or x = -y
When x = y, y^2 = -1/2 (rej.)
When x = -y, y^2 = 1/2 => y = 1/√2 or -1/√2 => x = -1/√2 or 1/√2
b = √(-i) = -1/√2 + i/√2 or 1/√2 - i/√2