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Simplifying (9 + -6i)(9 + i) = 0 Multiply (9 + -6i) * (9 + i) (9(9 + i) + -6i * (9 + i)) = 0 ((9 * 9 + i * 9) + -6i * (9 + i)) = 0 ((81 + 9i) + -6i * (9 + i)) = 0 (81 + 9i + (9 * -6i + i * -6i)) = 0 (81 + 9i + (-54i + -6i2)) = 0 Combine like terms: 9i + -54i = -45i (81 + -45i + -6i2) = 0 Solving 81 + -45i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -15i + -2i2) = 0 Factor a trinomial. 3((3 + -2i)(9 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Subproblem 2
Set the factor '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 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 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Solution
i = {1.5, -9}
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