Question 1081103: Given that (x + i y)^2 = i , find x and y where i is imaginary number,x and y are real.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Given that (x + i y)^2 = i , find x and y where i is imaginary number,x and y are real.
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(x + iy)^2 = i
x^2 + 2ixy + i^2y^2 = i
x^2 + 2ixy - y^2 = 0 + i
x^2 - y^2 = 0
2xy = 1 --> y = 1/(2x)
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x^2 - 1/(4x^2) = 0
x^4 - 1/4 = 0
x = -sqrt(2)/2, y = -2sqrt(2)
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x = +sqrt(2)/2, y = 2sqrt(2)
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