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Simplifying 9j2 + 12j + -12 = 0 Reorder the terms: -12 + 12j + 9j2 = 0 Solving -12 + 12j + 9j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 4j + 3j2) = 0 Factor a trinomial. 3((-2 + -1j)(2 + -3j)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1j)' equal to zero and attempt to solve: Simplifying -2 + -1j = 0 Solving -2 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1j = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1j = 0 + 2 -1j = 0 + 2 Combine like terms: 0 + 2 = 2 -1j = 2 Divide each side by '-1'. j = -2 Simplifying j = -2Subproblem 2
Set the factor '(2 + -3j)' equal to zero and attempt to solve: Simplifying 2 + -3j = 0 Solving 2 + -3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3j = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3j = 0 + -2 -3j = 0 + -2 Combine like terms: 0 + -2 = -2 -3j = -2 Divide each side by '-3'. j = 0.6666666667 Simplifying j = 0.6666666667Solution
j = {-2, 0.6666666667}
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