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Simplifying (9 + -2i)(4 + 6i) = 0 Multiply (9 + -2i) * (4 + 6i) (9(4 + 6i) + -2i * (4 + 6i)) = 0 ((4 * 9 + 6i * 9) + -2i * (4 + 6i)) = 0 ((36 + 54i) + -2i * (4 + 6i)) = 0 (36 + 54i + (4 * -2i + 6i * -2i)) = 0 (36 + 54i + (-8i + -12i2)) = 0 Combine like terms: 54i + -8i = 46i (36 + 46i + -12i2) = 0 Solving 36 + 46i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 23i + -6i2) = 0 Factor a trinomial. 2((9 + -2i)(2 + 3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -2i)' equal to zero and attempt to solve: Simplifying 9 + -2i = 0 Solving 9 + -2i = 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 + -2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2i = 0 + -9 -2i = 0 + -9 Combine like terms: 0 + -9 = -9 -2i = -9 Divide each side by '-2'. i = 4.5 Simplifying i = 4.5Subproblem 2
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 = -0.6666666667Solution
i = {4.5, -0.6666666667}
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