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Simplifying (-5 + 8i)(2 + 6i) = 0 Multiply (-5 + 8i) * (2 + 6i) (-5(2 + 6i) + 8i * (2 + 6i)) = 0 ((2 * -5 + 6i * -5) + 8i * (2 + 6i)) = 0 ((-10 + -30i) + 8i * (2 + 6i)) = 0 (-10 + -30i + (2 * 8i + 6i * 8i)) = 0 (-10 + -30i + (16i + 48i2)) = 0 Combine like terms: -30i + 16i = -14i (-10 + -14i + 48i2) = 0 Solving -10 + -14i + 48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -7i + 24i2) = 0 Factor a trinomial. 2((-1 + -3i)(5 + -8i)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Solution
i = {-0.3333333333, 0.625}
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