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Simplifying (5 + 3i) + -1(2 + xi) = 3 + -7i Remove parenthesis around (5 + 3i) 5 + 3i + -1(2 + xi) = 3 + -7i 5 + 3i + (2 * -1 + ix * -1) = 3 + -7i 5 + 3i + (-2 + -1ix) = 3 + -7i Reorder the terms: 5 + -2 + 3i + -1ix = 3 + -7i Combine like terms: 5 + -2 = 3 3 + 3i + -1ix = 3 + -7i Add '-3' to each side of the equation. 3 + 3i + -3 + -1ix = 3 + -3 + -7i Reorder the terms: 3 + -3 + 3i + -1ix = 3 + -3 + -7i Combine like terms: 3 + -3 = 0 0 + 3i + -1ix = 3 + -3 + -7i 3i + -1ix = 3 + -3 + -7i Combine like terms: 3 + -3 = 0 3i + -1ix = 0 + -7i 3i + -1ix = -7i Solving 3i + -1ix = -7i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '7i' to each side of the equation. 3i + 7i + -1ix = -7i + 7i Combine like terms: 3i + 7i = 10i 10i + -1ix = -7i + 7i Combine like terms: -7i + 7i = 0 10i + -1ix = 0 Factor out the Greatest Common Factor (GCF), 'i'. i(10 + -1x) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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