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Simplifying (9 + -4i)(9 + -18i) = 0 Multiply (9 + -4i) * (9 + -18i) (9(9 + -18i) + -4i * (9 + -18i)) = 0 ((9 * 9 + -18i * 9) + -4i * (9 + -18i)) = 0 ((81 + -162i) + -4i * (9 + -18i)) = 0 (81 + -162i + (9 * -4i + -18i * -4i)) = 0 (81 + -162i + (-36i + 72i2)) = 0 Combine like terms: -162i + -36i = -198i (81 + -198i + 72i2) = 0 Solving 81 + -198i + 72i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9'. 9(9 + -22i + 8i2) = 0 Factor a trinomial. 9((1 + -2i)(9 + -4i)) = 0 Ignore the factor 9.Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(9 + -4i)' equal to zero and attempt to solve: Simplifying 9 + -4i = 0 Solving 9 + -4i = 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 + -4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4i = 0 + -9 -4i = 0 + -9 Combine like terms: 0 + -9 = -9 -4i = -9 Divide each side by '-4'. i = 2.25 Simplifying i = 2.25Solution
i = {0.5, 2.25}
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