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Simplifying (7 + 5i)(6 + -4i) = 0 Multiply (7 + 5i) * (6 + -4i) (7(6 + -4i) + 5i * (6 + -4i)) = 0 ((6 * 7 + -4i * 7) + 5i * (6 + -4i)) = 0 ((42 + -28i) + 5i * (6 + -4i)) = 0 (42 + -28i + (6 * 5i + -4i * 5i)) = 0 (42 + -28i + (30i + -20i2)) = 0 Combine like terms: -28i + 30i = 2i (42 + 2i + -20i2) = 0 Solving 42 + 2i + -20i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + i + -10i2) = 0 Factor a trinomial. 2((3 + -2i)(7 + 5i)) = 0 Ignore the factor 2.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 + 5i)' equal to zero and attempt to solve: Simplifying 7 + 5i = 0 Solving 7 + 5i = 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 + 5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5i = 0 + -7 5i = 0 + -7 Combine like terms: 0 + -7 = -7 5i = -7 Divide each side by '5'. i = -1.4 Simplifying i = -1.4Solution
i = {1.5, -1.4}
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