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Simplifying (3 + 4j) * x(4 + -3j) = 0 Reorder the terms for easier multiplication: x(3 + 4j)(4 + -3j) = 0 Multiply (3 + 4j) * (4 + -3j) x(3(4 + -3j) + 4j * (4 + -3j)) = 0 x((4 * 3 + -3j * 3) + 4j * (4 + -3j)) = 0 x((12 + -9j) + 4j * (4 + -3j)) = 0 x(12 + -9j + (4 * 4j + -3j * 4j)) = 0 x(12 + -9j + (16j + -12j2)) = 0 Combine like terms: -9j + 16j = 7j x(12 + 7j + -12j2) = 0 (12 * x + 7j * x + -12j2 * x) = 0 Reorder the terms: (7jx + -12j2x + 12x) = 0 (7jx + -12j2x + 12x) = 0 Solving 7jx + -12j2x + 12x = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), 'x'. x(7j + -12j2 + 12) = 0 Factor a trinomial. x((-4j + -3)(3j + -4)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing j to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4j + -3)' equal to zero and attempt to solve: Simplifying -4j + -3 = 0 Reorder the terms: -3 + -4j = 0 Solving -3 + -4j = 0 Move all terms containing j to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4j = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4j = 0 + 3 -4j = 0 + 3 Combine like terms: 0 + 3 = 3 -4j = 3 Divide each side by '-4'. j = -0.75 Simplifying j = -0.75Subproblem 3
Set the factor '(3j + -4)' equal to zero and attempt to solve: Simplifying 3j + -4 = 0 Reorder the terms: -4 + 3j = 0 Solving -4 + 3j = 0 Move all terms containing j to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3j = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3j = 0 + 4 3j = 0 + 4 Combine like terms: 0 + 4 = 4 3j = 4 Divide each side by '3'. j = 1.333333333 Simplifying j = 1.333333333Solution
j = {-0.75, 1.333333333}
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