x^2+3xy+2+4i=-y^2+(x+y)iy

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Solution for x^2+3xy+2+4i=-y^2+(x+y)iy equation: 


Simplifying
x2 + 3xy + 2 + 4i = -1y2 + (x + y) * iy

Reorder the terms:
2 + 4i + 3xy + x2 = -1y2 + (x + y) * iy

Reorder the terms for easier multiplication:
2 + 4i + 3xy + x2 = -1y2 + iy(x + y)
2 + 4i + 3xy + x2 = -1y2 + (x * iy + y * iy)
2 + 4i + 3xy + x2 = -1y2 + (ixy + iy2)

Reorder the terms:
2 + 4i + 3xy + x2 = ixy + iy2 + -1y2

Solving
2 + 4i + 3xy + x2 = ixy + iy2 + -1y2

Solving for variable 'i'.

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

Add '-1ixy' to each side of the equation.
2 + 4i + 3xy + -1ixy + x2 = ixy + iy2 + -1ixy + -1y2

Reorder the terms:
2 + 4i + -1ixy + 3xy + x2 = ixy + iy2 + -1ixy + -1y2

Reorder the terms:
2 + 4i + -1ixy + 3xy + x2 = ixy + -1ixy + iy2 + -1y2

Combine like terms: ixy + -1ixy = 0
2 + 4i + -1ixy + 3xy + x2 = 0 + iy2 + -1y2
2 + 4i + -1ixy + 3xy + x2 = iy2 + -1y2

Add '-1iy2' to each side of the equation.
2 + 4i + -1ixy + 3xy + -1iy2 + x2 = iy2 + -1iy2 + -1y2

Reorder the terms:
2 + 4i + -1ixy + -1iy2 + 3xy + x2 = iy2 + -1iy2 + -1y2

Combine like terms: iy2 + -1iy2 = 0
2 + 4i + -1ixy + -1iy2 + 3xy + x2 = 0 + -1y2
2 + 4i + -1ixy + -1iy2 + 3xy + x2 = -1y2

Add '-2' to each side of the equation.
2 + 4i + -1ixy + -1iy2 + 3xy + -2 + x2 = -2 + -1y2

Reorder the terms:
2 + -2 + 4i + -1ixy + -1iy2 + 3xy + x2 = -2 + -1y2

Combine like terms: 2 + -2 = 0
0 + 4i + -1ixy + -1iy2 + 3xy + x2 = -2 + -1y2
4i + -1ixy + -1iy2 + 3xy + x2 = -2 + -1y2

Add '-3xy' to each side of the equation.
4i + -1ixy + -1iy2 + 3xy + -3xy + x2 = -2 + -3xy + -1y2

Combine like terms: 3xy + -3xy = 0
4i + -1ixy + -1iy2 + 0 + x2 = -2 + -3xy + -1y2
4i + -1ixy + -1iy2 + x2 = -2 + -3xy + -1y2

Add '-1x2' to each side of the equation.
4i + -1ixy + -1iy2 + x2 + -1x2 = -2 + -3xy + -1x2 + -1y2

Combine like terms: x2 + -1x2 = 0
4i + -1ixy + -1iy2 + 0 = -2 + -3xy + -1x2 + -1y2
4i + -1ixy + -1iy2 = -2 + -3xy + -1x2 + -1y2

Reorder the terms:
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = -2 + -3xy + -1x2 + -1y2 + 2 + 3xy + x2 + y2

Reorder the terms:
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = -2 + 2 + -3xy + 3xy + -1x2 + x2 + -1y2 + y2

Combine like terms: -2 + 2 = 0
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = 0 + -3xy + 3xy + -1x2 + x2 + -1y2 + y2
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = -3xy + 3xy + -1x2 + x2 + -1y2 + y2

Combine like terms: -3xy + 3xy = 0
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = 0 + -1x2 + x2 + -1y2 + y2
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = -1x2 + x2 + -1y2 + y2

Combine like terms: -1x2 + x2 = 0
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = 0 + -1y2 + y2
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
2 + 4i + -1ixy + -1iy2 + 3xy + x2 + y2 = 0

The solution to this equation could not be determined.

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