(x^2-y^2-2x-y+3)+i(2xy+x-2y-1)=0

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Solution for (x^2-y^2-2x-y+3)+i(2xy+x-2y-1)=0 equation: 


Simplifying
(x2 + -1y2 + -2x + -1y + 3) + i(2xy + x + -2y + -1) = 0

Reorder the terms:
(3 + -2x + x2 + -1y + -1y2) + i(2xy + x + -2y + -1) = 0

Remove parenthesis around (3 + -2x + x2 + -1y + -1y2)
3 + -2x + x2 + -1y + -1y2 + i(2xy + x + -2y + -1) = 0

Reorder the terms:
3 + -2x + x2 + -1y + -1y2 + i(-1 + x + 2xy + -2y) = 0
3 + -2x + x2 + -1y + -1y2 + (-1 * i + x * i + 2xy * i + -2y * i) = 0
3 + -2x + x2 + -1y + -1y2 + (-1i + ix + 2ixy + -2iy) = 0

Reorder the terms:
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0

Solving
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -3 + -1y2 = 0 + -3

Reorder the terms:
3 + -3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + -3
-1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = -3

Add '2x' to each side of the equation.
-1i + ix + 2ixy + -2iy + -2x + x2 + -1y + 2x + -1y2 = -3 + 2x

Reorder the terms:
-1i + ix + 2ixy + -2iy + -2x + 2x + x2 + -1y + -1y2 = -3 + 2x

Combine like terms: -2x + 2x = 0
-1i + ix + 2ixy + -2iy + 0 + x2 + -1y + -1y2 = -3 + 2x
-1i + ix + 2ixy + -2iy + x2 + -1y + -1y2 = -3 + 2x

Add '-1x2' to each side of the equation.
-1i + ix + 2ixy + -2iy + x2 + -1y + -1x2 + -1y2 = -3 + 2x + -1x2

Reorder the terms:
-1i + ix + 2ixy + -2iy + x2 + -1x2 + -1y + -1y2 = -3 + 2x + -1x2

Combine like terms: x2 + -1x2 = 0
-1i + ix + 2ixy + -2iy + 0 + -1y + -1y2 = -3 + 2x + -1x2
-1i + ix + 2ixy + -2iy + -1y + -1y2 = -3 + 2x + -1x2

Add 'y' to each side of the equation.
-1i + ix + 2ixy + -2iy + -1y + y + -1y2 = -3 + 2x + -1x2 + y

Combine like terms: -1y + y = 0
-1i + ix + 2ixy + -2iy + 0 + -1y2 = -3 + 2x + -1x2 + y
-1i + ix + 2ixy + -2iy + -1y2 = -3 + 2x + -1x2 + y

Add 'y2' to each side of the equation.
-1i + ix + 2ixy + -2iy + -1y2 + y2 = -3 + 2x + -1x2 + y + y2

Combine like terms: -1y2 + y2 = 0
-1i + ix + 2ixy + -2iy + 0 = -3 + 2x + -1x2 + y + y2
-1i + ix + 2ixy + -2iy = -3 + 2x + -1x2 + y + y2

Reorder the terms:
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = -3 + 2x + -1x2 + y + y2 + 3 + -2x + x2 + -1y + -1y2

Reorder the terms:
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = -3 + 3 + 2x + -2x + -1x2 + x2 + y + -1y + y2 + -1y2

Combine like terms: -3 + 3 = 0
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + 2x + -2x + -1x2 + x2 + y + -1y + y2 + -1y2
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 2x + -2x + -1x2 + x2 + y + -1y + y2 + -1y2

Combine like terms: 2x + -2x = 0
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + -1x2 + x2 + y + -1y + y2 + -1y2
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = -1x2 + x2 + y + -1y + y2 + -1y2

Combine like terms: -1x2 + x2 = 0
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + y + -1y + y2 + -1y2
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = y + -1y + y2 + -1y2

Combine like terms: y + -1y = 0
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0 + y2 + -1y2
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
3 + -1i + ix + 2ixy + -2iy + -2x + x2 + -1y + -1y2 = 0

The solution to this equation could not be determined.

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