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