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Simplifying (5 + -4i)(2 + 6i) = 0 Multiply (5 + -4i) * (2 + 6i) (5(2 + 6i) + -4i * (2 + 6i)) = 0 ((2 * 5 + 6i * 5) + -4i * (2 + 6i)) = 0 ((10 + 30i) + -4i * (2 + 6i)) = 0 (10 + 30i + (2 * -4i + 6i * -4i)) = 0 (10 + 30i + (-8i + -24i2)) = 0 Combine like terms: 30i + -8i = 22i (10 + 22i + -24i2) = 0 Solving 10 + 22i + -24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 11i + -12i2) = 0 Factor a trinomial. 2((5 + -4i)(1 + 3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Subproblem 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 = {1.25, -0.3333333333}
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