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Simplifying (9 + 6i)(7 + 4i) = 0 Multiply (9 + 6i) * (7 + 4i) (9(7 + 4i) + 6i * (7 + 4i)) = 0 ((7 * 9 + 4i * 9) + 6i * (7 + 4i)) = 0 ((63 + 36i) + 6i * (7 + 4i)) = 0 (63 + 36i + (7 * 6i + 4i * 6i)) = 0 (63 + 36i + (42i + 24i2)) = 0 Combine like terms: 36i + 42i = 78i (63 + 78i + 24i2) = 0 Solving 63 + 78i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + 26i + 8i2) = 0 Factor a trinomial. 3((7 + 4i)(3 + 2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 4i)' equal to zero and attempt to solve: Simplifying 7 + 4i = 0 Solving 7 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4i = 0 + -7 4i = 0 + -7 Combine like terms: 0 + -7 = -7 4i = -7 Divide each side by '4'. i = -1.75 Simplifying i = -1.75Subproblem 2
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 = -1.5Solution
i = {-1.75, -1.5}
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