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Simplifying (3 + 9i)(3 + 9i) = 0 Multiply (3 + 9i) * (3 + 9i) (3(3 + 9i) + 9i * (3 + 9i)) = 0 ((3 * 3 + 9i * 3) + 9i * (3 + 9i)) = 0 ((9 + 27i) + 9i * (3 + 9i)) = 0 (9 + 27i + (3 * 9i + 9i * 9i)) = 0 (9 + 27i + (27i + 81i2)) = 0 Combine like terms: 27i + 27i = 54i (9 + 54i + 81i2) = 0 Solving 9 + 54i + 81i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + 6i + 9i2) = 0 Factor a trinomial. 9((1 + 3i)(1 + 3i)) = 0 Ignore the factor 9.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 '(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 = -0.3333333333Solution
i = {-0.3333333333, -0.3333333333}
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