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Simplifying (6 + -9i)(9 + i) = 0 Multiply (6 + -9i) * (9 + i) (6(9 + i) + -9i * (9 + i)) = 0 ((9 * 6 + i * 6) + -9i * (9 + i)) = 0 ((54 + 6i) + -9i * (9 + i)) = 0 (54 + 6i + (9 * -9i + i * -9i)) = 0 (54 + 6i + (-81i + -9i2)) = 0 Combine like terms: 6i + -81i = -75i (54 + -75i + -9i2) = 0 Solving 54 + -75i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + -25i + -3i2) = 0 Factor a trinomial. 3((2 + -3i)(9 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 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 = {0.6666666667, -9}
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