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Simplifying i(4 + -6i)(4 + -6i) = 0 Multiply (4 + -6i) * (4 + -6i) i(4(4 + -6i) + -6i * (4 + -6i)) = 0 i((4 * 4 + -6i * 4) + -6i * (4 + -6i)) = 0 i((16 + -24i) + -6i * (4 + -6i)) = 0 i(16 + -24i + (4 * -6i + -6i * -6i)) = 0 i(16 + -24i + (-24i + 36i2)) = 0 Combine like terms: -24i + -24i = -48i i(16 + -48i + 36i2) = 0 (16 * i + -48i * i + 36i2 * i) = 0 (16i + -48i2 + 36i3) = 0 Solving 16i + -48i2 + 36i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4i'. 4i(4 + -12i + 9i2) = 0 Factor a trinomial. 4i((2 + -3i)(2 + -3i)) = 0 Ignore the factor 4.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 '(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 = 0.6666666667Subproblem 3
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 = {0, 0.6666666667, 0.6666666667}
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