(x+iy)*(x+iy)=1

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Solution for (x+iy)*(x+iy)=1 equation: 


Simplifying
(x + iy)(x + iy) = 1

Reorder the terms:
(iy + x)(x + iy) = 1

Reorder the terms:
(iy + x)(iy + x) = 1

Multiply (iy + x) * (iy + x)
(iy(iy + x) + x(iy + x)) = 1
((iy * iy + x * iy) + x(iy + x)) = 1

Reorder the terms:
((ixy + i2y2) + x(iy + x)) = 1
((ixy + i2y2) + x(iy + x)) = 1
(ixy + i2y2 + (iy * x + x * x)) = 1
(ixy + i2y2 + (ixy + x2)) = 1

Reorder the terms:
(ixy + ixy + i2y2 + x2) = 1

Combine like terms: ixy + ixy = 2ixy
(2ixy + i2y2 + x2) = 1

Solving
2ixy + i2y2 + x2 = 1

Solving for variable 'i'.

Reorder the terms:
-1 + 2ixy + i2y2 + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2ixy + i2y2 + x2 = 0

The solution to this equation could not be determined.

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