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Simplifying (5 + 6i)(4 + 8i) = 0 Multiply (5 + 6i) * (4 + 8i) (5(4 + 8i) + 6i * (4 + 8i)) = 0 ((4 * 5 + 8i * 5) + 6i * (4 + 8i)) = 0 ((20 + 40i) + 6i * (4 + 8i)) = 0 (20 + 40i + (4 * 6i + 8i * 6i)) = 0 (20 + 40i + (24i + 48i2)) = 0 Combine like terms: 40i + 24i = 64i (20 + 64i + 48i2) = 0 Solving 20 + 64i + 48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 16i + 12i2) = 0 Factor a trinomial. 4((5 + 6i)(1 + 2i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 6i)' equal to zero and attempt to solve: Simplifying 5 + 6i = 0 Solving 5 + 6i = 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 + 6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6i = 0 + -5 6i = 0 + -5 Combine like terms: 0 + -5 = -5 6i = -5 Divide each side by '6'. i = -0.8333333333 Simplifying i = -0.8333333333Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-0.8333333333, -0.5}
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