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