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Simplifying (6 + -8i)(2 + 8i) = 0 Multiply (6 + -8i) * (2 + 8i) (6(2 + 8i) + -8i * (2 + 8i)) = 0 ((2 * 6 + 8i * 6) + -8i * (2 + 8i)) = 0 ((12 + 48i) + -8i * (2 + 8i)) = 0 (12 + 48i + (2 * -8i + 8i * -8i)) = 0 (12 + 48i + (-16i + -64i2)) = 0 Combine like terms: 48i + -16i = 32i (12 + 32i + -64i2) = 0 Solving 12 + 32i + -64i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 8i + -16i2) = 0 Factor a trinomial. 4((3 + -4i)(1 + 4i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve: Simplifying 1 + 4i = 0 Solving 1 + 4i = 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 + 4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4i = 0 + -1 4i = 0 + -1 Combine like terms: 0 + -1 = -1 4i = -1 Divide each side by '4'. i = -0.25 Simplifying i = -0.25Solution
i = {0.75, -0.25}
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