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Simplifying (8 + 2i)(9 + i) = 0 Multiply (8 + 2i) * (9 + i) (8(9 + i) + 2i * (9 + i)) = 0 ((9 * 8 + i * 8) + 2i * (9 + i)) = 0 ((72 + 8i) + 2i * (9 + i)) = 0 (72 + 8i + (9 * 2i + i * 2i)) = 0 (72 + 8i + (18i + 2i2)) = 0 Combine like terms: 8i + 18i = 26i (72 + 26i + 2i2) = 0 Solving 72 + 26i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 13i + i2) = 0 Factor a trinomial. 2((9 + i)(4 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Subproblem 2
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 = -4Solution
i = {-9, -4}
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