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