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Simplifying (8 + 9i)(5 + i) = 0 Multiply (8 + 9i) * (5 + i) (8(5 + i) + 9i * (5 + i)) = 0 ((5 * 8 + i * 8) + 9i * (5 + i)) = 0 ((40 + 8i) + 9i * (5 + i)) = 0 (40 + 8i + (5 * 9i + i * 9i)) = 0 (40 + 8i + (45i + 9i2)) = 0 Combine like terms: 8i + 45i = 53i (40 + 53i + 9i2) = 0 Solving 40 + 53i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + i)(8 + 9i) = 0Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Subproblem 2
Set the factor '(8 + 9i)' equal to zero and attempt to solve: Simplifying 8 + 9i = 0 Solving 8 + 9i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 9i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9i = 0 + -8 9i = 0 + -8 Combine like terms: 0 + -8 = -8 9i = -8 Divide each side by '9'. i = -0.8888888889 Simplifying i = -0.8888888889Solution
i = {-5, -0.8888888889}
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