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Simplifying (3 + -2i) + -1(2x + yi) = 7 + 6i Remove parenthesis around (3 + -2i) 3 + -2i + -1(2x + yi) = 7 + 6i Reorder the terms: 3 + -2i + -1(iy + 2x) = 7 + 6i 3 + -2i + (iy * -1 + 2x * -1) = 7 + 6i 3 + -2i + (-1iy + -2x) = 7 + 6i Solving 3 + -2i + -1iy + -2x = 7 + 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. 3 + -2i + -1iy + -6i + -2x = 7 + 6i + -6i Reorder the terms: 3 + -2i + -6i + -1iy + -2x = 7 + 6i + -6i Combine like terms: -2i + -6i = -8i 3 + -8i + -1iy + -2x = 7 + 6i + -6i Combine like terms: 6i + -6i = 0 3 + -8i + -1iy + -2x = 7 + 0 3 + -8i + -1iy + -2x = 7 Add '-3' to each side of the equation. 3 + -8i + -1iy + -3 + -2x = 7 + -3 Reorder the terms: 3 + -3 + -8i + -1iy + -2x = 7 + -3 Combine like terms: 3 + -3 = 0 0 + -8i + -1iy + -2x = 7 + -3 -8i + -1iy + -2x = 7 + -3 Combine like terms: 7 + -3 = 4 -8i + -1iy + -2x = 4 Add '2x' to each side of the equation. -8i + -1iy + -2x + 2x = 4 + 2x Combine like terms: -2x + 2x = 0 -8i + -1iy + 0 = 4 + 2x -8i + -1iy = 4 + 2x Reorder the terms: -4 + -8i + -1iy + -2x = 4 + 2x + -4 + -2x Reorder the terms: -4 + -8i + -1iy + -2x = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -4 + -8i + -1iy + -2x = 0 + 2x + -2x -4 + -8i + -1iy + -2x = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + -8i + -1iy + -2x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 8i + iy + 2x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 8i + iy + 2x)' equal to zero and attempt to solve: Simplifying 4 + 8i + iy + 2x = 0 Solving 4 + 8i + iy + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 8i + iy + -4 + 2x = 0 + -4 Reorder the terms: 4 + -4 + 8i + iy + 2x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8i + iy + 2x = 0 + -4 8i + iy + 2x = 0 + -4 Combine like terms: 0 + -4 = -4 8i + iy + 2x = -4 Add '-2x' to each side of the equation. 8i + iy + 2x + -2x = -4 + -2x Combine like terms: 2x + -2x = 0 8i + iy + 0 = -4 + -2x 8i + iy = -4 + -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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