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