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Simplifying (7 + -4i)(6 + 4i) = 0 Multiply (7 + -4i) * (6 + 4i) (7(6 + 4i) + -4i * (6 + 4i)) = 0 ((6 * 7 + 4i * 7) + -4i * (6 + 4i)) = 0 ((42 + 28i) + -4i * (6 + 4i)) = 0 (42 + 28i + (6 * -4i + 4i * -4i)) = 0 (42 + 28i + (-24i + -16i2)) = 0 Combine like terms: 28i + -24i = 4i (42 + 4i + -16i2) = 0 Solving 42 + 4i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 2i + -8i2) = 0 Factor a trinomial. 2((7 + -4i)(3 + 2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -4i)' equal to zero and attempt to solve: Simplifying 7 + -4i = 0 Solving 7 + -4i = 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 + -4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4i = 0 + -7 -4i = 0 + -7 Combine like terms: 0 + -7 = -7 -4i = -7 Divide each side by '-4'. i = 1.75 Simplifying i = 1.75Subproblem 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 = {1.75, -1.5}
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