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Simplifying (-5 + -9i)(6 + 4i) = 0 Multiply (-5 + -9i) * (6 + 4i) (-5(6 + 4i) + -9i * (6 + 4i)) = 0 ((6 * -5 + 4i * -5) + -9i * (6 + 4i)) = 0 ((-30 + -20i) + -9i * (6 + 4i)) = 0 (-30 + -20i + (6 * -9i + 4i * -9i)) = 0 (-30 + -20i + (-54i + -36i2)) = 0 Combine like terms: -20i + -54i = -74i (-30 + -74i + -36i2) = 0 Solving -30 + -74i + -36i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(15 + 37i + 18i2) = 0 Factor a trinomial. -2((3 + 2i)(5 + 9i)) = 0 Ignore the factor -2.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 '(5 + 9i)' equal to zero and attempt to solve: Simplifying 5 + 9i = 0 Solving 5 + 9i = 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 + 9i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9i = 0 + -5 9i = 0 + -5 Combine like terms: 0 + -5 = -5 9i = -5 Divide each side by '9'. i = -0.5555555556 Simplifying i = -0.5555555556Solution
i = {-1.5, -0.5555555556}
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