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Simplifying (5 + -4i)(6 + 4i) = 0 Multiply (5 + -4i) * (6 + 4i) (5(6 + 4i) + -4i * (6 + 4i)) = 0 ((6 * 5 + 4i * 5) + -4i * (6 + 4i)) = 0 ((30 + 20i) + -4i * (6 + 4i)) = 0 (30 + 20i + (6 * -4i + 4i * -4i)) = 0 (30 + 20i + (-24i + -16i2)) = 0 Combine like terms: 20i + -24i = -4i (30 + -4i + -16i2) = 0 Solving 30 + -4i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -2i + -8i2) = 0 Factor a trinomial. 2((5 + -4i)(3 + 2i)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.25Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {1.25, -1.5}
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