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Simplifying i(9 + 6i)(9 + -6i) = 0 Multiply (9 + 6i) * (9 + -6i) i(9(9 + -6i) + 6i * (9 + -6i)) = 0 i((9 * 9 + -6i * 9) + 6i * (9 + -6i)) = 0 i((81 + -54i) + 6i * (9 + -6i)) = 0 i(81 + -54i + (9 * 6i + -6i * 6i)) = 0 i(81 + -54i + (54i + -36i2)) = 0 Combine like terms: -54i + 54i = 0 i(81 + 0 + -36i2) = 0 i(81 + -36i2) = 0 (81 * i + -36i2 * i) = 0 (81i + -36i3) = 0 Solving 81i + -36i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9i'. 9i(9 + -4i2) = 0 Factor a difference between two squares. 9i((3 + 2i)(3 + -2i)) = 0 Ignore the factor 9.Subproblem 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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