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Simplifying (6 + -3i)(6 + -1i) = 0 Multiply (6 + -3i) * (6 + -1i) (6(6 + -1i) + -3i * (6 + -1i)) = 0 ((6 * 6 + -1i * 6) + -3i * (6 + -1i)) = 0 ((36 + -6i) + -3i * (6 + -1i)) = 0 (36 + -6i + (6 * -3i + -1i * -3i)) = 0 (36 + -6i + (-18i + 3i2)) = 0 Combine like terms: -6i + -18i = -24i (36 + -24i + 3i2) = 0 Solving 36 + -24i + 3i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -8i + i2) = 0 Factor a trinomial. 3((2 + -1i)(6 + -1i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(6 + -1i)' equal to zero and attempt to solve: Simplifying 6 + -1i = 0 Solving 6 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1i = 0 + -6 -1i = 0 + -6 Combine like terms: 0 + -6 = -6 -1i = -6 Divide each side by '-1'. i = 6 Simplifying i = 6Solution
i = {2, 6}
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