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Simplifying (9 + -9i)(8 + 2i) = 0 Multiply (9 + -9i) * (8 + 2i) (9(8 + 2i) + -9i * (8 + 2i)) = 0 ((8 * 9 + 2i * 9) + -9i * (8 + 2i)) = 0 ((72 + 18i) + -9i * (8 + 2i)) = 0 (72 + 18i + (8 * -9i + 2i * -9i)) = 0 (72 + 18i + (-72i + -18i2)) = 0 Combine like terms: 18i + -72i = -54i (72 + -54i + -18i2) = 0 Solving 72 + -54i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '18'. 18(4 + -3i + -1i2) = 0 Factor a trinomial. 18((1 + -1i)(4 + i)) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, -4}
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