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Simplifying (2 + 8i)(9 + 8i) = 0 Multiply (2 + 8i) * (9 + 8i) (2(9 + 8i) + 8i * (9 + 8i)) = 0 ((9 * 2 + 8i * 2) + 8i * (9 + 8i)) = 0 ((18 + 16i) + 8i * (9 + 8i)) = 0 (18 + 16i + (9 * 8i + 8i * 8i)) = 0 (18 + 16i + (72i + 64i2)) = 0 Combine like terms: 16i + 72i = 88i (18 + 88i + 64i2) = 0 Solving 18 + 88i + 64i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 44i + 32i2) = 0 Factor a trinomial. 2((9 + 8i)(1 + 4i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 8i)' equal to zero and attempt to solve: Simplifying 9 + 8i = 0 Solving 9 + 8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 8i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8i = 0 + -9 8i = 0 + -9 Combine like terms: 0 + -9 = -9 8i = -9 Divide each side by '8'. i = -1.125 Simplifying i = -1.125Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve: Simplifying 1 + 4i = 0 Solving 1 + 4i = 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 + 4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4i = 0 + -1 4i = 0 + -1 Combine like terms: 0 + -1 = -1 4i = -1 Divide each side by '4'. i = -0.25 Simplifying i = -0.25Solution
i = {-1.125, -0.25}
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