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Simplifying (3 + 2i)(2 + -14i) = 0 Multiply (3 + 2i) * (2 + -14i) (3(2 + -14i) + 2i * (2 + -14i)) = 0 ((2 * 3 + -14i * 3) + 2i * (2 + -14i)) = 0 ((6 + -42i) + 2i * (2 + -14i)) = 0 (6 + -42i + (2 * 2i + -14i * 2i)) = 0 (6 + -42i + (4i + -28i2)) = 0 Combine like terms: -42i + 4i = -38i (6 + -38i + -28i2) = 0 Solving 6 + -38i + -28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -19i + -14i2) = 0 Factor a trinomial. 2((1 + -7i)(3 + 2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -7i)' equal to zero and attempt to solve: Simplifying 1 + -7i = 0 Solving 1 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7i = 0 + -1 -7i = 0 + -1 Combine like terms: 0 + -1 = -1 -7i = -1 Divide each side by '-7'. i = 0.1428571429 Simplifying i = 0.1428571429Subproblem 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 = {0.1428571429, -1.5}
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