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Simplifying (4j + -3)(5j + 8) = 0 Reorder the terms: (-3 + 4j)(5j + 8) = 0 Reorder the terms: (-3 + 4j)(8 + 5j) = 0 Multiply (-3 + 4j) * (8 + 5j) (-3(8 + 5j) + 4j * (8 + 5j)) = 0 ((8 * -3 + 5j * -3) + 4j * (8 + 5j)) = 0 ((-24 + -15j) + 4j * (8 + 5j)) = 0 (-24 + -15j + (8 * 4j + 5j * 4j)) = 0 (-24 + -15j + (32j + 20j2)) = 0 Combine like terms: -15j + 32j = 17j (-24 + 17j + 20j2) = 0 Solving -24 + 17j + 20j2 = 0 Solving for variable 'j'. Factor a trinomial. (-8 + -5j)(3 + -4j) = 0Subproblem 1
Set the factor '(-8 + -5j)' equal to zero and attempt to solve: Simplifying -8 + -5j = 0 Solving -8 + -5j = 0 Move all terms containing j to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5j = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5j = 0 + 8 -5j = 0 + 8 Combine like terms: 0 + 8 = 8 -5j = 8 Divide each side by '-5'. j = -1.6 Simplifying j = -1.6Subproblem 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 = {-1.6, 0.75}
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