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Simplifying (6 + -4i)(2 + 6i) = 0 Multiply (6 + -4i) * (2 + 6i) (6(2 + 6i) + -4i * (2 + 6i)) = 0 ((2 * 6 + 6i * 6) + -4i * (2 + 6i)) = 0 ((12 + 36i) + -4i * (2 + 6i)) = 0 (12 + 36i + (2 * -4i + 6i * -4i)) = 0 (12 + 36i + (-8i + -24i2)) = 0 Combine like terms: 36i + -8i = 28i (12 + 28i + -24i2) = 0 Solving 12 + 28i + -24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 7i + -6i2) = 0 Factor a trinomial. 4((3 + -2i)(1 + 3i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Subproblem 2
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 = -0.3333333333Solution
i = {1.5, -0.3333333333}
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