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Simplifying 12j2 + -32j + 5 = 0 Reorder the terms: 5 + -32j + 12j2 = 0 Solving 5 + -32j + 12j2 = 0 Solving for variable 'j'. Factor a trinomial. (1 + -6j)(5 + -2j) = 0Subproblem 1
Set the factor '(1 + -6j)' equal to zero and attempt to solve: Simplifying 1 + -6j = 0 Solving 1 + -6j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6j = 0 + -1 -6j = 0 + -1 Combine like terms: 0 + -1 = -1 -6j = -1 Divide each side by '-6'. j = 0.1666666667 Simplifying j = 0.1666666667Subproblem 2
Set the factor '(5 + -2j)' equal to zero and attempt to solve: Simplifying 5 + -2j = 0 Solving 5 + -2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2j = 0 + -5 -2j = 0 + -5 Combine like terms: 0 + -5 = -5 -2j = -5 Divide each side by '-2'. j = 2.5 Simplifying j = 2.5Solution
j = {0.1666666667, 2.5}
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