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Simplifying (5 + -2i) + (x * 4i) = 7 + -6i Remove parenthesis around (5 + -2i) 5 + -2i + (x * 4i) = 7 + -6i Reorder the terms for easier multiplication: 5 + -2i + (4x * i) = 7 + -6i Multiply x * i 5 + -2i + (4ix) = 7 + -6i Solving 5 + -2i + (4ix) = 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. 5 + -2i + 6i + (4ix) = 7 + -6i + 6i Combine like terms: -2i + 6i = 4i 5 + 4i + (4ix) = 7 + -6i + 6i Combine like terms: -6i + 6i = 0 5 + 4i + (4ix) = 7 + 0 5 + 4i + (4ix) = 7 Add '-5' to each side of the equation. 5 + 4i + -5 + (4ix) = 7 + -5 Reorder the terms: 5 + -5 + 4i + (4ix) = 7 + -5 Combine like terms: 5 + -5 = 0 0 + 4i + (4ix) = 7 + -5 4i + (4ix) = 7 + -5 Combine like terms: 7 + -5 = 2 4i + (4ix) = 2 Reorder the terms: -2 + 4i + (4ix) = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 4i + (4ix) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2i + (2ix)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2i + (2ix))' equal to zero and attempt to solve: Simplifying -1 + 2i + (2ix) = 0 Solving -1 + 2i + (2ix) = 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 + 1 + (2ix) = 0 + 1 Reorder the terms: -1 + 1 + 2i + (2ix) = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2i + (2ix) = 0 + 1 2i + (2ix) = 0 + 1 Combine like terms: 0 + 1 = 1 2i + (2ix) = 1 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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