(x+iy-1+3i)(x-iy+1-3i)=0

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Solution for (x+iy-1+3i)(x-iy+1-3i)=0 equation: 


Simplifying
(x + iy + -1 + 3i)(x + -1iy + 1 + -3i) = 0

Reorder the terms:
(-1 + 3i + iy + x)(x + -1iy + 1 + -3i) = 0

Reorder the terms:
(-1 + 3i + iy + x)(1 + -3i + -1iy + x) = 0

Multiply (-1 + 3i + iy + x) * (1 + -3i + -1iy + x)
(-1(1 + -3i + -1iy + x) + 3i * (1 + -3i + -1iy + x) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0
((1 * -1 + -3i * -1 + -1iy * -1 + x * -1) + 3i * (1 + -3i + -1iy + x) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0
((-1 + 3i + 1iy + -1x) + 3i * (1 + -3i + -1iy + x) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0
(-1 + 3i + 1iy + -1x + (1 * 3i + -3i * 3i + -1iy * 3i + x * 3i) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0

Reorder the terms:
(-1 + 3i + 1iy + -1x + (3i + 3ix + -9i2 + -3i2y) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0
(-1 + 3i + 1iy + -1x + (3i + 3ix + -9i2 + -3i2y) + iy(1 + -3i + -1iy + x) + x(1 + -3i + -1iy + x)) = 0
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + (1 * iy + -3i * iy + -1iy * iy + x * iy) + x(1 + -3i + -1iy + x)) = 0

Reorder the terms:
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + (ixy + 1iy + -3i2y + -1i2y2) + x(1 + -3i + -1iy + x)) = 0
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + (ixy + 1iy + -3i2y + -1i2y2) + x(1 + -3i + -1iy + x)) = 0
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + ixy + 1iy + -3i2y + -1i2y2 + (1 * x + -3i * x + -1iy * x + x * x)) = 0

Reorder the terms:
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + ixy + 1iy + -3i2y + -1i2y2 + (-3ix + -1ixy + 1x + x2)) = 0
(-1 + 3i + 1iy + -1x + 3i + 3ix + -9i2 + -3i2y + ixy + 1iy + -3i2y + -1i2y2 + (-3ix + -1ixy + 1x + x2)) = 0

Reorder the terms:
(-1 + 3i + 3i + 3ix + -3ix + ixy + -1ixy + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: 3i + 3i = 6i
(-1 + 6i + 3ix + -3ix + ixy + -1ixy + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: 3ix + -3ix = 0
(-1 + 6i + 0 + ixy + -1ixy + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0
(-1 + 6i + ixy + -1ixy + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: ixy + -1ixy = 0
(-1 + 6i + 0 + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0
(-1 + 6i + 1iy + 1iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: 1iy + 1iy = 2iy
(-1 + 6i + 2iy + -9i2 + -3i2y + -3i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: -3i2y + -3i2y = -6i2y
(-1 + 6i + 2iy + -9i2 + -6i2y + -1i2y2 + -1x + 1x + x2) = 0

Combine like terms: -1x + 1x = 0
(-1 + 6i + 2iy + -9i2 + -6i2y + -1i2y2 + 0 + x2) = 0
(-1 + 6i + 2iy + -9i2 + -6i2y + -1i2y2 + x2) = 0

Solving
-1 + 6i + 2iy + -9i2 + -6i2y + -1i2y2 + x2 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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