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Simplifying 3(x + iy) = 8 + -12i + -1(x + -1iy) Reorder the terms: 3(iy + x) = 8 + -12i + -1(x + -1iy) (iy * 3 + x * 3) = 8 + -12i + -1(x + -1iy) (3iy + 3x) = 8 + -12i + -1(x + -1iy) Reorder the terms: 3iy + 3x = 8 + -12i + -1(-1iy + x) 3iy + 3x = 8 + -12i + (-1iy * -1 + x * -1) 3iy + 3x = 8 + -12i + (1iy + -1x) Solving 3iy + 3x = 8 + -12i + 1iy + -1x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12i' to each side of the equation. 3iy + 12i + 3x = 8 + -12i + 1iy + 12i + -1x Reorder the terms: 12i + 3iy + 3x = 8 + -12i + 1iy + 12i + -1x Reorder the terms: 12i + 3iy + 3x = 8 + -12i + 12i + 1iy + -1x Combine like terms: -12i + 12i = 0 12i + 3iy + 3x = 8 + 0 + 1iy + -1x 12i + 3iy + 3x = 8 + 1iy + -1x Add '-1iy' to each side of the equation. 12i + 3iy + -1iy + 3x = 8 + 1iy + -1iy + -1x Combine like terms: 3iy + -1iy = 2iy 12i + 2iy + 3x = 8 + 1iy + -1iy + -1x Combine like terms: 1iy + -1iy = 0 12i + 2iy + 3x = 8 + 0 + -1x 12i + 2iy + 3x = 8 + -1x Add '-3x' to each side of the equation. 12i + 2iy + 3x + -3x = 8 + -1x + -3x Combine like terms: 3x + -3x = 0 12i + 2iy + 0 = 8 + -1x + -3x 12i + 2iy = 8 + -1x + -3x Combine like terms: -1x + -3x = -4x 12i + 2iy = 8 + -4x Reorder the terms: -8 + 12i + 2iy + 4x = 8 + -4x + -8 + 4x Reorder the terms: -8 + 12i + 2iy + 4x = 8 + -8 + -4x + 4x Combine like terms: 8 + -8 = 0 -8 + 12i + 2iy + 4x = 0 + -4x + 4x -8 + 12i + 2iy + 4x = -4x + 4x Combine like terms: -4x + 4x = 0 -8 + 12i + 2iy + 4x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 6i + iy + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 6i + iy + 2x)' equal to zero and attempt to solve: Simplifying -4 + 6i + iy + 2x = 0 Solving -4 + 6i + iy + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 6i + iy + 4 + 2x = 0 + 4 Reorder the terms: -4 + 4 + 6i + iy + 2x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6i + iy + 2x = 0 + 4 6i + iy + 2x = 0 + 4 Combine like terms: 0 + 4 = 4 6i + iy + 2x = 4 Add '-2x' to each side of the equation. 6i + iy + 2x + -2x = 4 + -2x Combine like terms: 2x + -2x = 0 6i + iy + 0 = 4 + -2x 6i + iy = 4 + -2x 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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