x^2+2xyi-y^2=i

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Solution for x^2+2xyi-y^2=i equation:


Simplifying
x2 + 2xyi + -1y2 = i

Reorder the terms:
2ixy + x2 + -1y2 = i

Solving
2ixy + x2 + -1y2 = i

Solving for variable 'i'.

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

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

Reorder the terms:
-1i + 2ixy + x2 + -1y2 = i + -1i

Combine like terms: i + -1i = 0
-1i + 2ixy + x2 + -1y2 = 0

Add '-1x2' to each side of the equation.
-1i + 2ixy + x2 + -1x2 + -1y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-1i + 2ixy + 0 + -1y2 = 0 + -1x2
-1i + 2ixy + -1y2 = 0 + -1x2
Remove the zero:
-1i + 2ixy + -1y2 = -1x2

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

Combine like terms: -1y2 + y2 = 0
-1i + 2ixy + 0 = -1x2 + y2
-1i + 2ixy = -1x2 + y2

Reorder the terms:
-1i + 2ixy + x2 + -1y2 = -1x2 + x2 + y2 + -1y2

Combine like terms: -1x2 + x2 = 0
-1i + 2ixy + x2 + -1y2 = 0 + y2 + -1y2
-1i + 2ixy + x2 + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-1i + 2ixy + x2 + -1y2 = 0

The solution to this equation could not be determined.

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