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Simplifying (3 + -3i)(5 + 6i) = 0 Multiply (3 + -3i) * (5 + 6i) (3(5 + 6i) + -3i * (5 + 6i)) = 0 ((5 * 3 + 6i * 3) + -3i * (5 + 6i)) = 0 ((15 + 18i) + -3i * (5 + 6i)) = 0 (15 + 18i + (5 * -3i + 6i * -3i)) = 0 (15 + 18i + (-15i + -18i2)) = 0 Combine like terms: 18i + -15i = 3i (15 + 3i + -18i2) = 0 Solving 15 + 3i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + i + -6i2) = 0 Factor a trinomial. 3((1 + -1i)(5 + 6i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, -0.8333333333}
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