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Simplifying (8 + 10i)(5 + -8i) = 0 Multiply (8 + 10i) * (5 + -8i) (8(5 + -8i) + 10i * (5 + -8i)) = 0 ((5 * 8 + -8i * 8) + 10i * (5 + -8i)) = 0 ((40 + -64i) + 10i * (5 + -8i)) = 0 (40 + -64i + (5 * 10i + -8i * 10i)) = 0 (40 + -64i + (50i + -80i2)) = 0 Combine like terms: -64i + 50i = -14i (40 + -14i + -80i2) = 0 Solving 40 + -14i + -80i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -7i + -40i2) = 0 Factor a trinomial. 2((5 + -8i)(4 + 5i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.625Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Solution
i = {0.625, -0.8}
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