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Simplifying -120 + 24j2 = -32j Solving -120 + 24j2 = -32j Solving for variable 'j'. Reorder the terms: -120 + 32j + 24j2 = -32j + 32j Combine like terms: -32j + 32j = 0 -120 + 32j + 24j2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-15 + 4j + 3j2) = 0 Factor a trinomial. 8((-3 + -1j)(5 + -3j)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -1j)' equal to zero and attempt to solve: Simplifying -3 + -1j = 0 Solving -3 + -1j = 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 + -1j = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1j = 0 + 3 -1j = 0 + 3 Combine like terms: 0 + 3 = 3 -1j = 3 Divide each side by '-1'. j = -3 Simplifying j = -3Subproblem 2
Set the factor '(5 + -3j)' equal to zero and attempt to solve: Simplifying 5 + -3j = 0 Solving 5 + -3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3j = 0 + -5 -3j = 0 + -5 Combine like terms: 0 + -5 = -5 -3j = -5 Divide each side by '-3'. j = 1.666666667 Simplifying j = 1.666666667Solution
j = {-3, 1.666666667}
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