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Simplifying (2 + -4i)(6 + 6i) = 0 Multiply (2 + -4i) * (6 + 6i) (2(6 + 6i) + -4i * (6 + 6i)) = 0 ((6 * 2 + 6i * 2) + -4i * (6 + 6i)) = 0 ((12 + 12i) + -4i * (6 + 6i)) = 0 (12 + 12i + (6 * -4i + 6i * -4i)) = 0 (12 + 12i + (-24i + -24i2)) = 0 Combine like terms: 12i + -24i = -12i (12 + -12i + -24i2) = 0 Solving 12 + -12i + -24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '12'. 12(1 + -1i + -2i2) = 0 Factor a trinomial. 12((1 + -2i)(1 + i)) = 0 Ignore the factor 12.Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {0.5, -1}
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