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Simplifying (4 + 8i)(5 + -1i) = 0 Multiply (4 + 8i) * (5 + -1i) (4(5 + -1i) + 8i * (5 + -1i)) = 0 ((5 * 4 + -1i * 4) + 8i * (5 + -1i)) = 0 ((20 + -4i) + 8i * (5 + -1i)) = 0 (20 + -4i + (5 * 8i + -1i * 8i)) = 0 (20 + -4i + (40i + -8i2)) = 0 Combine like terms: -4i + 40i = 36i (20 + 36i + -8i2) = 0 Solving 20 + 36i + -8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 9i + -2i2) = 0 Factor a trinomial. 4((5 + -1i)(1 + 2i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 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 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 5Subproblem 2
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 = -0.5Solution
i = {5, -0.5}
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