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Simplifying (-6 + -3i)(5 + 6i) = 0 Multiply (-6 + -3i) * (5 + 6i) (-6(5 + 6i) + -3i * (5 + 6i)) = 0 ((5 * -6 + 6i * -6) + -3i * (5 + 6i)) = 0 ((-30 + -36i) + -3i * (5 + 6i)) = 0 (-30 + -36i + (5 * -3i + 6i * -3i)) = 0 (-30 + -36i + (-15i + -18i2)) = 0 Combine like terms: -36i + -15i = -51i (-30 + -51i + -18i2) = 0 Solving -30 + -51i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-3'. -3(10 + 17i + 6i2) = 0 Factor a trinomial. -3((2 + i)(5 + 6i)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Subproblem 2
Set the factor '(5 + 6i)' equal to zero and attempt to solve: Simplifying 5 + 6i = 0 Solving 5 + 6i = 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 + 6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6i = 0 + -5 6i = 0 + -5 Combine like terms: 0 + -5 = -5 6i = -5 Divide each side by '6'. i = -0.8333333333 Simplifying i = -0.8333333333Solution
i = {-2, -0.8333333333}
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