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Simplifying (3 + 8i)(9 + -1i) = 0 Multiply (3 + 8i) * (9 + -1i) (3(9 + -1i) + 8i * (9 + -1i)) = 0 ((9 * 3 + -1i * 3) + 8i * (9 + -1i)) = 0 ((27 + -3i) + 8i * (9 + -1i)) = 0 (27 + -3i + (9 * 8i + -1i * 8i)) = 0 (27 + -3i + (72i + -8i2)) = 0 Combine like terms: -3i + 72i = 69i (27 + 69i + -8i2) = 0 Solving 27 + 69i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -1i)(3 + 8i) = 0Subproblem 1
Set the factor '(9 + -1i)' equal to zero and attempt to solve: Simplifying 9 + -1i = 0 Solving 9 + -1i = 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 + -1i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i = 0 + -9 -1i = 0 + -9 Combine like terms: 0 + -9 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9Subproblem 2
Set the factor '(3 + 8i)' equal to zero and attempt to solve: Simplifying 3 + 8i = 0 Solving 3 + 8i = 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 + 8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8i = 0 + -3 8i = 0 + -3 Combine like terms: 0 + -3 = -3 8i = -3 Divide each side by '8'. i = -0.375 Simplifying i = -0.375Solution
i = {9, -0.375}
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