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Simplifying (-4 + 2i)(8 + -6i) = 0 Multiply (-4 + 2i) * (8 + -6i) (-4(8 + -6i) + 2i * (8 + -6i)) = 0 ((8 * -4 + -6i * -4) + 2i * (8 + -6i)) = 0 ((-32 + 24i) + 2i * (8 + -6i)) = 0 (-32 + 24i + (8 * 2i + -6i * 2i)) = 0 (-32 + 24i + (16i + -12i2)) = 0 Combine like terms: 24i + 16i = 40i (-32 + 40i + -12i2) = 0 Solving -32 + 40i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 10i + -3i2) = 0 Factor a trinomial. 4((-2 + i)(4 + -3i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve: Simplifying -2 + i = 0 Solving -2 + i = 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 + i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i = 0 + 2 i = 0 + 2 Combine like terms: 0 + 2 = 2 i = 2 Simplifying i = 2Subproblem 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 = {2, 1.333333333}
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