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Simplifying (8 + 6i)(-5 + 7i) = 0 Multiply (8 + 6i) * (-5 + 7i) (8(-5 + 7i) + 6i * (-5 + 7i)) = 0 ((-5 * 8 + 7i * 8) + 6i * (-5 + 7i)) = 0 ((-40 + 56i) + 6i * (-5 + 7i)) = 0 (-40 + 56i + (-5 * 6i + 7i * 6i)) = 0 (-40 + 56i + (-30i + 42i2)) = 0 Combine like terms: 56i + -30i = 26i (-40 + 26i + 42i2) = 0 Solving -40 + 26i + 42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 13i + 21i2) = 0 Factor a trinomial. 2((-4 + -3i)(5 + -7i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -3i)' equal to zero and attempt to solve: Simplifying -4 + -3i = 0 Solving -4 + -3i = 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 + -3i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3i = 0 + 4 -3i = 0 + 4 Combine like terms: 0 + 4 = 4 -3i = 4 Divide each side by '-3'. i = -1.333333333 Simplifying i = -1.333333333Subproblem 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 = {-1.333333333, 0.7142857143}
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