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Simplifying (4 + i)(2 + -6i) = 0 Multiply (4 + i) * (2 + -6i) (4(2 + -6i) + i(2 + -6i)) = 0 ((2 * 4 + -6i * 4) + i(2 + -6i)) = 0 ((8 + -24i) + i(2 + -6i)) = 0 (8 + -24i + (2 * i + -6i * i)) = 0 (8 + -24i + (2i + -6i2)) = 0 Combine like terms: -24i + 2i = -22i (8 + -22i + -6i2) = 0 Solving 8 + -22i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -11i + -3i2) = 0 Factor a trinomial. 2((1 + -3i)(4 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 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 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Solution
i = {0.3333333333, -4}
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