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Simplifying (6 + -8i)(9 + 2i) = 0 Multiply (6 + -8i) * (9 + 2i) (6(9 + 2i) + -8i * (9 + 2i)) = 0 ((9 * 6 + 2i * 6) + -8i * (9 + 2i)) = 0 ((54 + 12i) + -8i * (9 + 2i)) = 0 (54 + 12i + (9 * -8i + 2i * -8i)) = 0 (54 + 12i + (-72i + -16i2)) = 0 Combine like terms: 12i + -72i = -60i (54 + -60i + -16i2) = 0 Solving 54 + -60i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -30i + -8i2) = 0 Factor a trinomial. 2((3 + -4i)(9 + 2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Subproblem 2
Set the factor '(9 + 2i)' equal to zero and attempt to solve: Simplifying 9 + 2i = 0 Solving 9 + 2i = 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 + 2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2i = 0 + -9 2i = 0 + -9 Combine like terms: 0 + -9 = -9 2i = -9 Divide each side by '2'. i = -4.5 Simplifying i = -4.5Solution
i = {0.75, -4.5}
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