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Simplifying (4 + -2i)(5 + 7i) = 0 Multiply (4 + -2i) * (5 + 7i) (4(5 + 7i) + -2i * (5 + 7i)) = 0 ((5 * 4 + 7i * 4) + -2i * (5 + 7i)) = 0 ((20 + 28i) + -2i * (5 + 7i)) = 0 (20 + 28i + (5 * -2i + 7i * -2i)) = 0 (20 + 28i + (-10i + -14i2)) = 0 Combine like terms: 28i + -10i = 18i (20 + 18i + -14i2) = 0 Solving 20 + 18i + -14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 9i + -7i2) = 0 Factor a trinomial. 2((2 + -1i)(5 + 7i)) = 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 '(5 + 7i)' equal to zero and attempt to solve: Simplifying 5 + 7i = 0 Solving 5 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7i = 0 + -5 7i = 0 + -5 Combine like terms: 0 + -5 = -5 7i = -5 Divide each side by '7'. i = -0.7142857143 Simplifying i = -0.7142857143Solution
i = {2, -0.7142857143}
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