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Simplifying (9 + -3i)(5 + 2i) = 0 Multiply (9 + -3i) * (5 + 2i) (9(5 + 2i) + -3i * (5 + 2i)) = 0 ((5 * 9 + 2i * 9) + -3i * (5 + 2i)) = 0 ((45 + 18i) + -3i * (5 + 2i)) = 0 (45 + 18i + (5 * -3i + 2i * -3i)) = 0 (45 + 18i + (-15i + -6i2)) = 0 Combine like terms: 18i + -15i = 3i (45 + 3i + -6i2) = 0 Solving 45 + 3i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + i + -2i2) = 0 Factor a trinomial. 3((3 + -1i)(5 + 2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 2
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 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 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Solution
i = {3, -2.5}
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