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Simplifying (8 + 2i)(5 + 8i) = 0 Multiply (8 + 2i) * (5 + 8i) (8(5 + 8i) + 2i * (5 + 8i)) = 0 ((5 * 8 + 8i * 8) + 2i * (5 + 8i)) = 0 ((40 + 64i) + 2i * (5 + 8i)) = 0 (40 + 64i + (5 * 2i + 8i * 2i)) = 0 (40 + 64i + (10i + 16i2)) = 0 Combine like terms: 64i + 10i = 74i (40 + 74i + 16i2) = 0 Solving 40 + 74i + 16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 37i + 8i2) = 0 Factor a trinomial. 2((4 + i)(5 + 8i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Subproblem 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 = {-4, -0.625}
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