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Simplifying 3x + -3yi = 12 + -15i Reorder the terms: -3iy + 3x = 12 + -15i Solving -3iy + 3x = 12 + -15i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '15i' to each side of the equation. -3iy + 15i + 3x = 12 + -15i + 15i Reorder the terms: 15i + -3iy + 3x = 12 + -15i + 15i Combine like terms: -15i + 15i = 0 15i + -3iy + 3x = 12 + 0 15i + -3iy + 3x = 12 Add '-3x' to each side of the equation. 15i + -3iy + 3x + -3x = 12 + -3x Combine like terms: 3x + -3x = 0 15i + -3iy + 0 = 12 + -3x 15i + -3iy = 12 + -3x Reorder the terms: -12 + 15i + -3iy + 3x = 12 + -3x + -12 + 3x Reorder the terms: -12 + 15i + -3iy + 3x = 12 + -12 + -3x + 3x Combine like terms: 12 + -12 = 0 -12 + 15i + -3iy + 3x = 0 + -3x + 3x -12 + 15i + -3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -12 + 15i + -3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5i + -1iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5i + -1iy + x)' equal to zero and attempt to solve: Simplifying -4 + 5i + -1iy + x = 0 Solving -4 + 5i + -1iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 5i + -1iy + 4 + x = 0 + 4 Reorder the terms: -4 + 4 + 5i + -1iy + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5i + -1iy + x = 0 + 4 5i + -1iy + x = 0 + 4 Combine like terms: 0 + 4 = 4 5i + -1iy + x = 4 Add '-1x' to each side of the equation. 5i + -1iy + x + -1x = 4 + -1x Combine like terms: x + -1x = 0 5i + -1iy + 0 = 4 + -1x 5i + -1iy = 4 + -1x 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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