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Simplifying (4 + -6i)(4 + 8i) = 0 Multiply (4 + -6i) * (4 + 8i) (4(4 + 8i) + -6i * (4 + 8i)) = 0 ((4 * 4 + 8i * 4) + -6i * (4 + 8i)) = 0 ((16 + 32i) + -6i * (4 + 8i)) = 0 (16 + 32i + (4 * -6i + 8i * -6i)) = 0 (16 + 32i + (-24i + -48i2)) = 0 Combine like terms: 32i + -24i = 8i (16 + 8i + -48i2) = 0 Solving 16 + 8i + -48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8'. 8(2 + i + -6i2) = 0 Factor a trinomial. 8((2 + -3i)(1 + 2i)) = 0 Ignore the factor 8.Subproblem 1
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 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 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 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {0.6666666667, -0.5}
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