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Simplifying (7 + 2i)(9 + -6i) = 0 Multiply (7 + 2i) * (9 + -6i) (7(9 + -6i) + 2i * (9 + -6i)) = 0 ((9 * 7 + -6i * 7) + 2i * (9 + -6i)) = 0 ((63 + -42i) + 2i * (9 + -6i)) = 0 (63 + -42i + (9 * 2i + -6i * 2i)) = 0 (63 + -42i + (18i + -12i2)) = 0 Combine like terms: -42i + 18i = -24i (63 + -24i + -12i2) = 0 Solving 63 + -24i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + -8i + -4i2) = 0 Factor a trinomial. 3((3 + -2i)(7 + 2i)) = 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 '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 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 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {1.5, -3.5}
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