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Simplifying i(3 + 2i)(3 + 2i) = 0 Multiply (3 + 2i) * (3 + 2i) i(3(3 + 2i) + 2i * (3 + 2i)) = 0 i((3 * 3 + 2i * 3) + 2i * (3 + 2i)) = 0 i((9 + 6i) + 2i * (3 + 2i)) = 0 i(9 + 6i + (3 * 2i + 2i * 2i)) = 0 i(9 + 6i + (6i + 4i2)) = 0 Combine like terms: 6i + 6i = 12i i(9 + 12i + 4i2) = 0 (9 * i + 12i * i + 4i2 * i) = 0 (9i + 12i2 + 4i3) = 0 Solving 9i + 12i2 + 4i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(9 + 12i + 4i2) = 0 Factor a trinomial. i((3 + 2i)(3 + 2i)) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Subproblem 3
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {0, -1.5, -1.5}
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