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Simplifying 2x + -1y + (3y + -2xi) = 2 + -2i Reorder the terms: 2x + -1y + (-2ix + 3y) = 2 + -2i Remove parenthesis around (-2ix + 3y) 2x + -1y + -2ix + 3y = 2 + -2i Reorder the terms: -2ix + 2x + -1y + 3y = 2 + -2i Combine like terms: -1y + 3y = 2y -2ix + 2x + 2y = 2 + -2i Solving -2ix + 2x + 2y = 2 + -2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2i' to each side of the equation. -2ix + 2x + 2i + 2y = 2 + -2i + 2i Reorder the terms: 2i + -2ix + 2x + 2y = 2 + -2i + 2i Combine like terms: -2i + 2i = 0 2i + -2ix + 2x + 2y = 2 + 0 2i + -2ix + 2x + 2y = 2 Add '-2x' to each side of the equation. 2i + -2ix + 2x + -2x + 2y = 2 + -2x Combine like terms: 2x + -2x = 0 2i + -2ix + 0 + 2y = 2 + -2x 2i + -2ix + 2y = 2 + -2x Add '-2y' to each side of the equation. 2i + -2ix + 2y + -2y = 2 + -2x + -2y Combine like terms: 2y + -2y = 0 2i + -2ix + 0 = 2 + -2x + -2y 2i + -2ix = 2 + -2x + -2y Reorder the terms: -2 + 2i + -2ix + 2x + 2y = 2 + -2x + -2y + -2 + 2x + 2y Reorder the terms: -2 + 2i + -2ix + 2x + 2y = 2 + -2 + -2x + 2x + -2y + 2y Combine like terms: 2 + -2 = 0 -2 + 2i + -2ix + 2x + 2y = 0 + -2x + 2x + -2y + 2y -2 + 2i + -2ix + 2x + 2y = -2x + 2x + -2y + 2y Combine like terms: -2x + 2x = 0 -2 + 2i + -2ix + 2x + 2y = 0 + -2y + 2y -2 + 2i + -2ix + 2x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 -2 + 2i + -2ix + 2x + 2y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + i + -1ix + x + y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + i + -1ix + x + y)' equal to zero and attempt to solve: Simplifying -1 + i + -1ix + x + y = 0 Solving -1 + i + -1ix + x + y = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + i + -1ix + x + 1 + y = 0 + 1 Reorder the terms: -1 + 1 + i + -1ix + x + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + i + -1ix + x + y = 0 + 1 i + -1ix + x + y = 0 + 1 Combine like terms: 0 + 1 = 1 i + -1ix + x + y = 1 Add '-1x' to each side of the equation. i + -1ix + x + -1x + y = 1 + -1x Combine like terms: x + -1x = 0 i + -1ix + 0 + y = 1 + -1x i + -1ix + y = 1 + -1x Add '-1y' to each side of the equation. i + -1ix + y + -1y = 1 + -1x + -1y Combine like terms: y + -1y = 0 i + -1ix + 0 = 1 + -1x + -1y i + -1ix = 1 + -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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