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Simplifying (8 + 2i)(5 + -7i) = 0 Multiply (8 + 2i) * (5 + -7i) (8(5 + -7i) + 2i * (5 + -7i)) = 0 ((5 * 8 + -7i * 8) + 2i * (5 + -7i)) = 0 ((40 + -56i) + 2i * (5 + -7i)) = 0 (40 + -56i + (5 * 2i + -7i * 2i)) = 0 (40 + -56i + (10i + -14i2)) = 0 Combine like terms: -56i + 10i = -46i (40 + -46i + -14i2) = 0 Solving 40 + -46i + -14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -23i + -7i2) = 0 Factor a trinomial. 2((5 + -7i)(4 + i)) = 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 '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Solution
i = {0.7142857143, -4}
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