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Simplifying -6i(8 + -6i)(8 + -8i) = 0 Multiply (8 + -6i) * (8 + -8i) -6i(8(8 + -8i) + -6i * (8 + -8i)) = 0 -6i((8 * 8 + -8i * 8) + -6i * (8 + -8i)) = 0 -6i((64 + -64i) + -6i * (8 + -8i)) = 0 -6i(64 + -64i + (8 * -6i + -8i * -6i)) = 0 -6i(64 + -64i + (-48i + 48i2)) = 0 Combine like terms: -64i + -48i = -112i -6i(64 + -112i + 48i2) = 0 (64 * -6i + -112i * -6i + 48i2 * -6i) = 0 (-384i + 672i2 + -288i3) = 0 Solving -384i + 672i2 + -288i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '96i'. 96i(-4 + 7i + -3i2) = 0 Factor a trinomial. 96i((-4 + 3i)(1 + -1i)) = 0 Ignore the factor 96.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 '(-4 + 3i)' equal to zero and attempt to solve: Simplifying -4 + 3i = 0 Solving -4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3i = 0 + 4 3i = 0 + 4 Combine like terms: 0 + 4 = 4 3i = 4 Divide each side by '3'. i = 1.333333333 Simplifying i = 1.333333333Subproblem 3
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {0, 1.333333333, 1}
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