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Simplifying (9 + 8i)(9 + 8i) = 0 Multiply (9 + 8i) * (9 + 8i) (9(9 + 8i) + 8i * (9 + 8i)) = 0 ((9 * 9 + 8i * 9) + 8i * (9 + 8i)) = 0 ((81 + 72i) + 8i * (9 + 8i)) = 0 (81 + 72i + (9 * 8i + 8i * 8i)) = 0 (81 + 72i + (72i + 64i2)) = 0 Combine like terms: 72i + 72i = 144i (81 + 144i + 64i2) = 0 Solving 81 + 144i + 64i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + 8i)(9 + 8i) = 0Subproblem 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 '(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 = {-1.125, -1.125}
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