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Simplifying (7i + -2)(6i + 9) = 0 Reorder the terms: (-2 + 7i)(6i + 9) = 0 Reorder the terms: (-2 + 7i)(9 + 6i) = 0 Multiply (-2 + 7i) * (9 + 6i) (-2(9 + 6i) + 7i * (9 + 6i)) = 0 ((9 * -2 + 6i * -2) + 7i * (9 + 6i)) = 0 ((-18 + -12i) + 7i * (9 + 6i)) = 0 (-18 + -12i + (9 * 7i + 6i * 7i)) = 0 (-18 + -12i + (63i + 42i2)) = 0 Combine like terms: -12i + 63i = 51i (-18 + 51i + 42i2) = 0 Solving -18 + 51i + 42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 17i + 14i2) = 0 Factor a trinomial. 3((-3 + -2i)(2 + -7i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2i)' equal to zero and attempt to solve: Simplifying -3 + -2i = 0 Solving -3 + -2i = 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 + -2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2i = 0 + 3 -2i = 0 + 3 Combine like terms: 0 + 3 = 3 -2i = 3 Divide each side by '-2'. i = -1.5 Simplifying i = -1.5Subproblem 2
Set the factor '(2 + -7i)' equal to zero and attempt to solve: Simplifying 2 + -7i = 0 Solving 2 + -7i = 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 + -7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7i = 0 + -2 -7i = 0 + -2 Combine like terms: 0 + -2 = -2 -7i = -2 Divide each side by '-7'. i = 0.2857142857 Simplifying i = 0.2857142857Solution
i = {-1.5, 0.2857142857}
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