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Simplifying (3 + -9i)(3 + -1i) = 0 Multiply (3 + -9i) * (3 + -1i) (3(3 + -1i) + -9i * (3 + -1i)) = 0 ((3 * 3 + -1i * 3) + -9i * (3 + -1i)) = 0 ((9 + -3i) + -9i * (3 + -1i)) = 0 (9 + -3i + (3 * -9i + -1i * -9i)) = 0 (9 + -3i + (-27i + 9i2)) = 0 Combine like terms: -3i + -27i = -30i (9 + -30i + 9i2) = 0 Solving 9 + -30i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -10i + 3i2) = 0 Factor a trinomial. 3((1 + -3i)(3 + -1i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Subproblem 2
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 = 3Solution
i = {0.3333333333, 3}
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