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Simplifying (2 + -9i)(9 + -6i) = 0 Multiply (2 + -9i) * (9 + -6i) (2(9 + -6i) + -9i * (9 + -6i)) = 0 ((9 * 2 + -6i * 2) + -9i * (9 + -6i)) = 0 ((18 + -12i) + -9i * (9 + -6i)) = 0 (18 + -12i + (9 * -9i + -6i * -9i)) = 0 (18 + -12i + (-81i + 54i2)) = 0 Combine like terms: -12i + -81i = -93i (18 + -93i + 54i2) = 0 Solving 18 + -93i + 54i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -31i + 18i2) = 0 Factor a trinomial. 3((2 + -9i)(3 + -2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -9i)' equal to zero and attempt to solve: Simplifying 2 + -9i = 0 Solving 2 + -9i = 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 + -9i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9i = 0 + -2 -9i = 0 + -2 Combine like terms: 0 + -2 = -2 -9i = -2 Divide each side by '-9'. i = 0.2222222222 Simplifying i = 0.2222222222Subproblem 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 = {0.2222222222, 1.5}
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