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Simplifying (8 + -6i)(-4 + -4i) = 0 Multiply (8 + -6i) * (-4 + -4i) (8(-4 + -4i) + -6i * (-4 + -4i)) = 0 ((-4 * 8 + -4i * 8) + -6i * (-4 + -4i)) = 0 ((-32 + -32i) + -6i * (-4 + -4i)) = 0 (-32 + -32i + (-4 * -6i + -4i * -6i)) = 0 (-32 + -32i + (24i + 24i2)) = 0 Combine like terms: -32i + 24i = -8i (-32 + -8i + 24i2) = 0 Solving -32 + -8i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + -1i + 3i2) = 0 Factor a trinomial. 8((-1 + -1i)(4 + -3i)) = 0 Ignore the factor 8.Subproblem 1
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 = -1Subproblem 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 = 1.333333333Solution
i = {-1, 1.333333333}
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