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Simplifying (8 + -7i)(5 + -6i) = 0 Multiply (8 + -7i) * (5 + -6i) (8(5 + -6i) + -7i * (5 + -6i)) = 0 ((5 * 8 + -6i * 8) + -7i * (5 + -6i)) = 0 ((40 + -48i) + -7i * (5 + -6i)) = 0 (40 + -48i + (5 * -7i + -6i * -7i)) = 0 (40 + -48i + (-35i + 42i2)) = 0 Combine like terms: -48i + -35i = -83i (40 + -83i + 42i2) = 0 Solving 40 + -83i + 42i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(8 + -7i) = 0Subproblem 1
Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 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 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333Subproblem 2
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Solution
i = {0.8333333333, 1.142857143}
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