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Simplifying (x + yi) + (2(x + yi) + 3i) = 9 Reorder the terms: (iy + x) + (2(x + yi) + 3i) = 9 Remove parenthesis around (iy + x) iy + x + (2(x + yi) + 3i) = 9 Reorder the terms: iy + x + (2(iy + x) + 3i) = 9 iy + x + ((iy * 2 + x * 2) + 3i) = 9 iy + x + ((2iy + 2x) + 3i) = 9 Reorder the terms: iy + x + (3i + 2iy + 2x) = 9 Remove parenthesis around (3i + 2iy + 2x) iy + x + 3i + 2iy + 2x = 9 Reorder the terms: 3i + iy + 2iy + x + 2x = 9 Combine like terms: iy + 2iy = 3iy 3i + 3iy + x + 2x = 9 Combine like terms: x + 2x = 3x 3i + 3iy + 3x = 9 Solving 3i + 3iy + 3x = 9 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3x' to each side of the equation. 3i + 3iy + 3x + -3x = 9 + -3x Combine like terms: 3x + -3x = 0 3i + 3iy + 0 = 9 + -3x 3i + 3iy = 9 + -3x Reorder the terms: -9 + 3i + 3iy + 3x = 9 + -3x + -9 + 3x Reorder the terms: -9 + 3i + 3iy + 3x = 9 + -9 + -3x + 3x Combine like terms: 9 + -9 = 0 -9 + 3i + 3iy + 3x = 0 + -3x + 3x -9 + 3i + 3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -9 + 3i + 3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + i + iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + i + iy + x)' equal to zero and attempt to solve: Simplifying -3 + i + iy + x = 0 Solving -3 + i + iy + 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 + i + iy + 3 + x = 0 + 3 Reorder the terms: -3 + 3 + i + iy + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + i + iy + x = 0 + 3 i + iy + x = 0 + 3 Combine like terms: 0 + 3 = 3 i + iy + x = 3 Add '-1x' to each side of the equation. i + iy + x + -1x = 3 + -1x Combine like terms: x + -1x = 0 i + iy + 0 = 3 + -1x i + iy = 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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