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Simplifying (4 + -2i)(9 + i) = 0 Multiply (4 + -2i) * (9 + i) (4(9 + i) + -2i * (9 + i)) = 0 ((9 * 4 + i * 4) + -2i * (9 + i)) = 0 ((36 + 4i) + -2i * (9 + i)) = 0 (36 + 4i + (9 * -2i + i * -2i)) = 0 (36 + 4i + (-18i + -2i2)) = 0 Combine like terms: 4i + -18i = -14i (36 + -14i + -2i2) = 0 Solving 36 + -14i + -2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -7i + -1i2) = 0 Factor a trinomial. 2((2 + -1i)(9 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
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 = -9Solution
i = {2, -9}
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