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Simplifying (5 + 3i)(9 + 8i) = 0 Multiply (5 + 3i) * (9 + 8i) (5(9 + 8i) + 3i * (9 + 8i)) = 0 ((9 * 5 + 8i * 5) + 3i * (9 + 8i)) = 0 ((45 + 40i) + 3i * (9 + 8i)) = 0 (45 + 40i + (9 * 3i + 8i * 3i)) = 0 (45 + 40i + (27i + 24i2)) = 0 Combine like terms: 40i + 27i = 67i (45 + 67i + 24i2) = 0 Solving 45 + 67i + 24i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 3i)(9 + 8i) = 0Subproblem 1
Set the factor '(5 + 3i)' equal to zero and attempt to solve: Simplifying 5 + 3i = 0 Solving 5 + 3i = 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 + 3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3i = 0 + -5 3i = 0 + -5 Combine like terms: 0 + -5 = -5 3i = -5 Divide each side by '3'. i = -1.666666667 Simplifying i = -1.666666667Subproblem 2
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 = -1.125Solution
i = {-1.666666667, -1.125}
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