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Simplifying (6 + -8i)(2 + 7i) = 0 Multiply (6 + -8i) * (2 + 7i) (6(2 + 7i) + -8i * (2 + 7i)) = 0 ((2 * 6 + 7i * 6) + -8i * (2 + 7i)) = 0 ((12 + 42i) + -8i * (2 + 7i)) = 0 (12 + 42i + (2 * -8i + 7i * -8i)) = 0 (12 + 42i + (-16i + -56i2)) = 0 Combine like terms: 42i + -16i = 26i (12 + 26i + -56i2) = 0 Solving 12 + 26i + -56i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 13i + -28i2) = 0 Factor a trinomial. 2((3 + -4i)(2 + 7i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 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 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Subproblem 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 = {0.75, -0.2857142857}
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