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