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