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Simplifying (7 + 6i)(4 + -2i) = 0 Multiply (7 + 6i) * (4 + -2i) (7(4 + -2i) + 6i * (4 + -2i)) = 0 ((4 * 7 + -2i * 7) + 6i * (4 + -2i)) = 0 ((28 + -14i) + 6i * (4 + -2i)) = 0 (28 + -14i + (4 * 6i + -2i * 6i)) = 0 (28 + -14i + (24i + -12i2)) = 0 Combine like terms: -14i + 24i = 10i (28 + 10i + -12i2) = 0 Solving 28 + 10i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 5i + -6i2) = 0 Factor a trinomial. 2((2 + -1i)(7 + 6i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(7 + 6i)' equal to zero and attempt to solve: Simplifying 7 + 6i = 0 Solving 7 + 6i = 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 + 6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i = 0 + -7 6i = 0 + -7 Combine like terms: 0 + -7 = -7 6i = -7 Divide each side by '6'. i = -1.166666667 Simplifying i = -1.166666667Solution
i = {2, -1.166666667}
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