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Simplifying (12 + -5i)(7i + 5) = 0 Reorder the terms: (12 + -5i)(5 + 7i) = 0 Multiply (12 + -5i) * (5 + 7i) (12(5 + 7i) + -5i * (5 + 7i)) = 0 ((5 * 12 + 7i * 12) + -5i * (5 + 7i)) = 0 ((60 + 84i) + -5i * (5 + 7i)) = 0 (60 + 84i + (5 * -5i + 7i * -5i)) = 0 (60 + 84i + (-25i + -35i2)) = 0 Combine like terms: 84i + -25i = 59i (60 + 59i + -35i2) = 0 Solving 60 + 59i + -35i2 = 0 Solving for variable 'i'. Factor a trinomial. (12 + -5i)(5 + 7i) = 0Subproblem 1
Set the factor '(12 + -5i)' equal to zero and attempt to solve: Simplifying 12 + -5i = 0 Solving 12 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5i = 0 + -12 -5i = 0 + -12 Combine like terms: 0 + -12 = -12 -5i = -12 Divide each side by '-5'. i = 2.4 Simplifying i = 2.4Subproblem 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 = {2.4, -0.7142857143}
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