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Simplifying (6 + 3i)(9 + -1i) = 0 Multiply (6 + 3i) * (9 + -1i) (6(9 + -1i) + 3i * (9 + -1i)) = 0 ((9 * 6 + -1i * 6) + 3i * (9 + -1i)) = 0 ((54 + -6i) + 3i * (9 + -1i)) = 0 (54 + -6i + (9 * 3i + -1i * 3i)) = 0 (54 + -6i + (27i + -3i2)) = 0 Combine like terms: -6i + 27i = 21i (54 + 21i + -3i2) = 0 Solving 54 + 21i + -3i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 7i + -1i2) = 0 Factor a trinomial. 3((9 + -1i)(2 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -1i)' equal to zero and attempt to solve: Simplifying 9 + -1i = 0 Solving 9 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i = 0 + -9 -1i = 0 + -9 Combine like terms: 0 + -9 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9Subproblem 2
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 = -2Solution
i = {9, -2}
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