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Simplifying (2 + 3i)(3 + 3i) = 0 Multiply (2 + 3i) * (3 + 3i) (2(3 + 3i) + 3i * (3 + 3i)) = 0 ((3 * 2 + 3i * 2) + 3i * (3 + 3i)) = 0 ((6 + 6i) + 3i * (3 + 3i)) = 0 (6 + 6i + (3 * 3i + 3i * 3i)) = 0 (6 + 6i + (9i + 9i2)) = 0 Combine like terms: 6i + 9i = 15i (6 + 15i + 9i2) = 0 Solving 6 + 15i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 5i + 3i2) = 0 Factor a trinomial. 3((1 + i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Subproblem 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 = {-1, -0.6666666667}
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