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Simplifying (3 + 4j)(5 + -12j) = 0 Multiply (3 + 4j) * (5 + -12j) (3(5 + -12j) + 4j * (5 + -12j)) = 0 ((5 * 3 + -12j * 3) + 4j * (5 + -12j)) = 0 ((15 + -36j) + 4j * (5 + -12j)) = 0 (15 + -36j + (5 * 4j + -12j * 4j)) = 0 (15 + -36j + (20j + -48j2)) = 0 Combine like terms: -36j + 20j = -16j (15 + -16j + -48j2) = 0 Solving 15 + -16j + -48j2 = 0 Solving for variable 'j'. Factor a trinomial. (5 + -12j)(3 + 4j) = 0Subproblem 1
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 = 0.4166666667Subproblem 2
Set the factor '(3 + 4j)' equal to zero and attempt to solve: Simplifying 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 = -0.75Solution
j = {0.4166666667, -0.75}
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