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Simplifying (9 + -6i)(4 + i) = 0 Multiply (9 + -6i) * (4 + i) (9(4 + i) + -6i * (4 + i)) = 0 ((4 * 9 + i * 9) + -6i * (4 + i)) = 0 ((36 + 9i) + -6i * (4 + i)) = 0 (36 + 9i + (4 * -6i + i * -6i)) = 0 (36 + 9i + (-24i + -6i2)) = 0 Combine like terms: 9i + -24i = -15i (36 + -15i + -6i2) = 0 Solving 36 + -15i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -5i + -2i2) = 0 Factor a trinomial. 3((3 + -2i)(4 + 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 '(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 = {1.5, -4}
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