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Simplifying 12 + 3i = 2x + (2y + 1) * i Reorder the terms: 12 + 3i = 2x + (1 + 2y) * i Reorder the terms for easier multiplication: 12 + 3i = 2x + i(1 + 2y) 12 + 3i = 2x + (1 * i + 2y * i) 12 + 3i = 2x + (1i + 2iy) Reorder the terms: 12 + 3i = 1i + 2iy + 2x Solving 12 + 3i = 1i + 2iy + 2x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 12 + 3i + -1i = 1i + 2iy + -1i + 2x Combine like terms: 3i + -1i = 2i 12 + 2i = 1i + 2iy + -1i + 2x Reorder the terms: 12 + 2i = 1i + -1i + 2iy + 2x Combine like terms: 1i + -1i = 0 12 + 2i = 0 + 2iy + 2x 12 + 2i = 2iy + 2x Add '-2iy' to each side of the equation. 12 + 2i + -2iy = 2iy + -2iy + 2x Combine like terms: 2iy + -2iy = 0 12 + 2i + -2iy = 0 + 2x 12 + 2i + -2iy = 2x Add '-12' to each side of the equation. 12 + 2i + -12 + -2iy = -12 + 2x Reorder the terms: 12 + -12 + 2i + -2iy = -12 + 2x Combine like terms: 12 + -12 = 0 0 + 2i + -2iy = -12 + 2x 2i + -2iy = -12 + 2x Reorder the terms: 12 + 2i + -2iy + -2x = -12 + 2x + 12 + -2x Reorder the terms: 12 + 2i + -2iy + -2x = -12 + 12 + 2x + -2x Combine like terms: -12 + 12 = 0 12 + 2i + -2iy + -2x = 0 + 2x + -2x 12 + 2i + -2iy + -2x = 2x + -2x Combine like terms: 2x + -2x = 0 12 + 2i + -2iy + -2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + i + -1iy + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + i + -1iy + -1x)' equal to zero and attempt to solve: Simplifying 6 + i + -1iy + -1x = 0 Solving 6 + i + -1iy + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + i + -1iy + -6 + -1x = 0 + -6 Reorder the terms: 6 + -6 + i + -1iy + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + i + -1iy + -1x = 0 + -6 i + -1iy + -1x = 0 + -6 Combine like terms: 0 + -6 = -6 i + -1iy + -1x = -6 Add 'x' to each side of the equation. i + -1iy + -1x + x = -6 + x Combine like terms: -1x + x = 0 i + -1iy + 0 = -6 + x i + -1iy = -6 + x 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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