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

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


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

Multiply x * x
x2 + 3xy + 2 + 4i = -1y * -1y + (xy + y * y) * i

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

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

Multiply -1 * -1
2 + 4i + 3xy + x2 = 1y * y + (xy + y * y) * i

Multiply y * y
2 + 4i + 3xy + x2 = 1y2 + (xy + y * y) * i

Multiply y * y
2 + 4i + 3xy + x2 = 1y2 + (xy + y2) * i

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

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

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

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

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

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

The solution to this equation could not be determined.

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