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Simplifying (5 + -7i)(2 + 4i) = 0 Multiply (5 + -7i) * (2 + 4i) (5(2 + 4i) + -7i * (2 + 4i)) = 0 ((2 * 5 + 4i * 5) + -7i * (2 + 4i)) = 0 ((10 + 20i) + -7i * (2 + 4i)) = 0 (10 + 20i + (2 * -7i + 4i * -7i)) = 0 (10 + 20i + (-14i + -28i2)) = 0 Combine like terms: 20i + -14i = 6i (10 + 6i + -28i2) = 0 Solving 10 + 6i + -28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 3i + -14i2) = 0 Factor a trinomial. 2((5 + -7i)(1 + 2i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.7142857143Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {0.7142857143, -0.5}
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