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Simplifying (5 + 12j)(10 + 2j) = 0 Multiply (5 + 12j) * (10 + 2j) (5(10 + 2j) + 12j * (10 + 2j)) = 0 ((10 * 5 + 2j * 5) + 12j * (10 + 2j)) = 0 ((50 + 10j) + 12j * (10 + 2j)) = 0 (50 + 10j + (10 * 12j + 2j * 12j)) = 0 (50 + 10j + (120j + 24j2)) = 0 Combine like terms: 10j + 120j = 130j (50 + 130j + 24j2) = 0 Solving 50 + 130j + 24j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 65j + 12j2) = 0 Factor a trinomial. 2((5 + j)(5 + 12j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + j)' equal to zero and attempt to solve: Simplifying 5 + j = 0 Solving 5 + j = 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 + j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + j = 0 + -5 j = 0 + -5 Combine like terms: 0 + -5 = -5 j = -5 Simplifying j = -5Subproblem 2
Set the factor '(5 + 12j)' equal to zero and attempt to solve: Simplifying 5 + 12j = 0 Solving 5 + 12j = 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 + 12j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12j = 0 + -5 12j = 0 + -5 Combine like terms: 0 + -5 = -5 12j = -5 Divide each side by '12'. j = -0.4166666667 Simplifying j = -0.4166666667Solution
j = {-5, -0.4166666667}
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