(x-iy)(x+iy)=x^2+y^2

Solution for (x-iy)(x+iy)=x^2+y^2 equation:

Simplifying
(x + -1iy)(x + iy) = x2 + y2

Reorder the terms:
(-1iy + x)(x + iy) = x2 + y2

Reorder the terms:
(-1iy + x)(iy + x) = x2 + y2

Multiply (-1iy + x) * (iy + x)
(-1iy * (iy + x) + x(iy + x)) = x2 + y2
((iy * -1iy + x * -1iy) + x(iy + x)) = x2 + y2

Reorder the terms:
((-1ixy + -1i2y2) + x(iy + x)) = x2 + y2
((-1ixy + -1i2y2) + x(iy + x)) = x2 + y2
(-1ixy + -1i2y2 + (iy * x + x * x)) = x2 + y2
(-1ixy + -1i2y2 + (ixy + x2)) = x2 + y2

Reorder the terms:
(-1ixy + ixy + -1i2y2 + x2) = x2 + y2

Combine like terms: -1ixy + ixy = 0
(0 + -1i2y2 + x2) = x2 + y2
(-1i2y2 + x2) = x2 + y2

Add '-1x2' to each side of the equation.
-1i2y2 + x2 + -1x2 = x2 + -1x2 + y2

Combine like terms: x2 + -1x2 = 0
-1i2y2 + 0 = x2 + -1x2 + y2
-1i2y2 = x2 + -1x2 + y2

Combine like terms: x2 + -1x2 = 0
-1i2y2 = 0 + y2
-1i2y2 = y2

Solving
-1i2y2 = y2

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Divide each side by '-1y2'.
i2 = -1

Simplifying
i2 = -1

Reorder the terms:
1 + i2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + i2 = 0

The solution to this equation could not be determined.