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Simplifying (5 + -4i)(6 + 9i) = 0 Multiply (5 + -4i) * (6 + 9i) (5(6 + 9i) + -4i * (6 + 9i)) = 0 ((6 * 5 + 9i * 5) + -4i * (6 + 9i)) = 0 ((30 + 45i) + -4i * (6 + 9i)) = 0 (30 + 45i + (6 * -4i + 9i * -4i)) = 0 (30 + 45i + (-24i + -36i2)) = 0 Combine like terms: 45i + -24i = 21i (30 + 21i + -36i2) = 0 Solving 30 + 21i + -36i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 7i + -12i2) = 0 Factor a trinomial. 3((5 + -4i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Subproblem 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 = {1.25, -0.6666666667}
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