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