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Simplifying (9 + 5i)(4 + -2i) = 0 Multiply (9 + 5i) * (4 + -2i) (9(4 + -2i) + 5i * (4 + -2i)) = 0 ((4 * 9 + -2i * 9) + 5i * (4 + -2i)) = 0 ((36 + -18i) + 5i * (4 + -2i)) = 0 (36 + -18i + (4 * 5i + -2i * 5i)) = 0 (36 + -18i + (20i + -10i2)) = 0 Combine like terms: -18i + 20i = 2i (36 + 2i + -10i2) = 0 Solving 36 + 2i + -10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + i + -5i2) = 0 Factor a trinomial. 2((2 + -1i)(9 + 5i)) = 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 + 5i)' equal to zero and attempt to solve: Simplifying 9 + 5i = 0 Solving 9 + 5i = 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 + 5i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5i = 0 + -9 5i = 0 + -9 Combine like terms: 0 + -9 = -9 5i = -9 Divide each side by '5'. i = -1.8 Simplifying i = -1.8Solution
i = {2, -1.8}
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