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