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Simplifying (5 + 4i)(6 + -8i) = 0 Multiply (5 + 4i) * (6 + -8i) (5(6 + -8i) + 4i * (6 + -8i)) = 0 ((6 * 5 + -8i * 5) + 4i * (6 + -8i)) = 0 ((30 + -40i) + 4i * (6 + -8i)) = 0 (30 + -40i + (6 * 4i + -8i * 4i)) = 0 (30 + -40i + (24i + -32i2)) = 0 Combine like terms: -40i + 24i = -16i (30 + -16i + -32i2) = 0 Solving 30 + -16i + -32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -8i + -16i2) = 0 Factor a trinomial. 2((3 + -4i)(5 + 4i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Subproblem 2
Set the factor '(5 + 4i)' equal to zero and attempt to solve: Simplifying 5 + 4i = 0 Solving 5 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4i = 0 + -5 4i = 0 + -5 Combine like terms: 0 + -5 = -5 4i = -5 Divide each side by '4'. i = -1.25 Simplifying i = -1.25Solution
i = {0.75, -1.25}
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