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Simplifying (3j + -5)(4j + -3) = 0 Reorder the terms: (-5 + 3j)(4j + -3) = 0 Reorder the terms: (-5 + 3j)(-3 + 4j) = 0 Multiply (-5 + 3j) * (-3 + 4j) (-5(-3 + 4j) + 3j * (-3 + 4j)) = 0 ((-3 * -5 + 4j * -5) + 3j * (-3 + 4j)) = 0 ((15 + -20j) + 3j * (-3 + 4j)) = 0 (15 + -20j + (-3 * 3j + 4j * 3j)) = 0 (15 + -20j + (-9j + 12j2)) = 0 Combine like terms: -20j + -9j = -29j (15 + -29j + 12j2) = 0 Solving 15 + -29j + 12j2 = 0 Solving for variable 'j'. Factor a trinomial. (3 + -4j)(5 + -3j) = 0Subproblem 1
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 = 0.75Subproblem 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 = {0.75, 1.666666667}
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