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Simplifying 2x2 + -8y + (4y + -2x) * i = 4 + -2i Reorder the terms: 2x2 + -8y + (-2x + 4y) * i = 4 + -2i Reorder the terms for easier multiplication: 2x2 + -8y + i(-2x + 4y) = 4 + -2i 2x2 + -8y + (-2x * i + 4y * i) = 4 + -2i 2x2 + -8y + (-2ix + 4iy) = 4 + -2i Reorder the terms: -2ix + 4iy + 2x2 + -8y = 4 + -2i Solving -2ix + 4iy + 2x2 + -8y = 4 + -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 + 4iy + 2x2 + 2i + -8y = 4 + -2i + 2i Reorder the terms: 2i + -2ix + 4iy + 2x2 + -8y = 4 + -2i + 2i Combine like terms: -2i + 2i = 0 2i + -2ix + 4iy + 2x2 + -8y = 4 + 0 2i + -2ix + 4iy + 2x2 + -8y = 4 Add '-2x2' to each side of the equation. 2i + -2ix + 4iy + 2x2 + -2x2 + -8y = 4 + -2x2 Combine like terms: 2x2 + -2x2 = 0 2i + -2ix + 4iy + 0 + -8y = 4 + -2x2 2i + -2ix + 4iy + -8y = 4 + -2x2 Add '8y' to each side of the equation. 2i + -2ix + 4iy + -8y + 8y = 4 + -2x2 + 8y Combine like terms: -8y + 8y = 0 2i + -2ix + 4iy + 0 = 4 + -2x2 + 8y 2i + -2ix + 4iy = 4 + -2x2 + 8y Reorder the terms: -4 + 2i + -2ix + 4iy + 2x2 + -8y = 4 + -2x2 + 8y + -4 + 2x2 + -8y Reorder the terms: -4 + 2i + -2ix + 4iy + 2x2 + -8y = 4 + -4 + -2x2 + 2x2 + 8y + -8y Combine like terms: 4 + -4 = 0 -4 + 2i + -2ix + 4iy + 2x2 + -8y = 0 + -2x2 + 2x2 + 8y + -8y -4 + 2i + -2ix + 4iy + 2x2 + -8y = -2x2 + 2x2 + 8y + -8y Combine like terms: -2x2 + 2x2 = 0 -4 + 2i + -2ix + 4iy + 2x2 + -8y = 0 + 8y + -8y -4 + 2i + -2ix + 4iy + 2x2 + -8y = 8y + -8y Combine like terms: 8y + -8y = 0 -4 + 2i + -2ix + 4iy + 2x2 + -8y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + i + -1ix + 2iy + x2 + -4y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + i + -1ix + 2iy + x2 + -4y)' equal to zero and attempt to solve: Simplifying -2 + i + -1ix + 2iy + x2 + -4y = 0 Solving -2 + i + -1ix + 2iy + x2 + -4y = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + i + -1ix + 2iy + x2 + 2 + -4y = 0 + 2 Reorder the terms: -2 + 2 + i + -1ix + 2iy + x2 + -4y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i + -1ix + 2iy + x2 + -4y = 0 + 2 i + -1ix + 2iy + x2 + -4y = 0 + 2 Combine like terms: 0 + 2 = 2 i + -1ix + 2iy + x2 + -4y = 2 Add '-1x2' to each side of the equation. i + -1ix + 2iy + x2 + -1x2 + -4y = 2 + -1x2 Combine like terms: x2 + -1x2 = 0 i + -1ix + 2iy + 0 + -4y = 2 + -1x2 i + -1ix + 2iy + -4y = 2 + -1x2 Add '4y' to each side of the equation. i + -1ix + 2iy + -4y + 4y = 2 + -1x2 + 4y Combine like terms: -4y + 4y = 0 i + -1ix + 2iy + 0 = 2 + -1x2 + 4y i + -1ix + 2iy = 2 + -1x2 + 4y 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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