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Simplifying (3 + -2j)(2 + 4j) = 0 Multiply (3 + -2j) * (2 + 4j) (3(2 + 4j) + -2j * (2 + 4j)) = 0 ((2 * 3 + 4j * 3) + -2j * (2 + 4j)) = 0 ((6 + 12j) + -2j * (2 + 4j)) = 0 (6 + 12j + (2 * -2j + 4j * -2j)) = 0 (6 + 12j + (-4j + -8j2)) = 0 Combine like terms: 12j + -4j = 8j (6 + 8j + -8j2) = 0 Solving 6 + 8j + -8j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 4j + -4j2) = 0 Factor a trinomial. 2((3 + -2j)(1 + 2j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2j)' equal to zero and attempt to solve: Simplifying 3 + -2j = 0 Solving 3 + -2j = 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 + -2j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2j = 0 + -3 -2j = 0 + -3 Combine like terms: 0 + -3 = -3 -2j = -3 Divide each side by '-2'. j = 1.5 Simplifying j = 1.5Subproblem 2
Set the factor '(1 + 2j)' equal to zero and attempt to solve: Simplifying 1 + 2j = 0 Solving 1 + 2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2j = 0 + -1 2j = 0 + -1 Combine like terms: 0 + -1 = -1 2j = -1 Divide each side by '2'. j = -0.5 Simplifying j = -0.5Solution
j = {1.5, -0.5}
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