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Simplifying (9 + -8i)(4 + i) = 0 Multiply (9 + -8i) * (4 + i) (9(4 + i) + -8i * (4 + i)) = 0 ((4 * 9 + i * 9) + -8i * (4 + i)) = 0 ((36 + 9i) + -8i * (4 + i)) = 0 (36 + 9i + (4 * -8i + i * -8i)) = 0 (36 + 9i + (-32i + -8i2)) = 0 Combine like terms: 9i + -32i = -23i (36 + -23i + -8i2) = 0 Solving 36 + -23i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -8i)(4 + i) = 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 '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Solution
i = {1.125, -4}
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