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Simplifying (6 + 3i)(2 + 3i) = 0 Multiply (6 + 3i) * (2 + 3i) (6(2 + 3i) + 3i * (2 + 3i)) = 0 ((2 * 6 + 3i * 6) + 3i * (2 + 3i)) = 0 ((12 + 18i) + 3i * (2 + 3i)) = 0 (12 + 18i + (2 * 3i + 3i * 3i)) = 0 (12 + 18i + (6i + 9i2)) = 0 Combine like terms: 18i + 6i = 24i (12 + 24i + 9i2) = 0 Solving 12 + 24i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 8i + 3i2) = 0 Factor a trinomial. 3((2 + i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 2
Set the factor '(2 + 3i)' equal to zero and attempt to solve: Simplifying 2 + 3i = 0 Solving 2 + 3i = 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 + 3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3i = 0 + -2 3i = 0 + -2 Combine like terms: 0 + -2 = -2 3i = -2 Divide each side by '3'. i = -0.6666666667 Simplifying i = -0.6666666667Solution
i = {-2, -0.6666666667}
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