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Simplifying (9 + -6i) * xm = 9 + -6i Reorder the terms for easier multiplication: mx(9 + -6i) = 9 + -6i (9 * mx + -6i * mx) = 9 + -6i Reorder the terms: (-6imx + 9mx) = 9 + -6i (-6imx + 9mx) = 9 + -6i Solving -6imx + 9mx = 9 + -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. -6imx + 6i + 9mx = 9 + -6i + 6i Reorder the terms: 6i + -6imx + 9mx = 9 + -6i + 6i Combine like terms: -6i + 6i = 0 6i + -6imx + 9mx = 9 + 0 6i + -6imx + 9mx = 9 Add '-9mx' to each side of the equation. 6i + -6imx + 9mx + -9mx = 9 + -9mx Combine like terms: 9mx + -9mx = 0 6i + -6imx + 0 = 9 + -9mx 6i + -6imx = 9 + -9mx Reorder the terms: -9 + 6i + -6imx + 9mx = 9 + -9mx + -9 + 9mx Reorder the terms: -9 + 6i + -6imx + 9mx = 9 + -9 + -9mx + 9mx Combine like terms: 9 + -9 = 0 -9 + 6i + -6imx + 9mx = 0 + -9mx + 9mx -9 + 6i + -6imx + 9mx = -9mx + 9mx Combine like terms: -9mx + 9mx = 0 -9 + 6i + -6imx + 9mx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2i + -2imx + 3mx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 2i + -2imx + 3mx)' equal to zero and attempt to solve: Simplifying -3 + 2i + -2imx + 3mx = 0 Solving -3 + 2i + -2imx + 3mx = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 2i + -2imx + 3 + 3mx = 0 + 3 Reorder the terms: -3 + 3 + 2i + -2imx + 3mx = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2i + -2imx + 3mx = 0 + 3 2i + -2imx + 3mx = 0 + 3 Combine like terms: 0 + 3 = 3 2i + -2imx + 3mx = 3 Add '-3mx' to each side of the equation. 2i + -2imx + 3mx + -3mx = 3 + -3mx Combine like terms: 3mx + -3mx = 0 2i + -2imx + 0 = 3 + -3mx 2i + -2imx = 3 + -3mx 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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