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Simplifying (j + -9)(j + 2) = 0 Reorder the terms: (-9 + j)(j + 2) = 0 Reorder the terms: (-9 + j)(2 + j) = 0 Multiply (-9 + j) * (2 + j) (-9(2 + j) + j(2 + j)) = 0 ((2 * -9 + j * -9) + j(2 + j)) = 0 ((-18 + -9j) + j(2 + j)) = 0 (-18 + -9j + (2 * j + j * j)) = 0 (-18 + -9j + (2j + j2)) = 0 Combine like terms: -9j + 2j = -7j (-18 + -7j + j2) = 0 Solving -18 + -7j + j2 = 0 Solving for variable 'j'. Factor a trinomial. (-2 + -1j)(9 + -1j) = 0Subproblem 1
Set the factor '(-2 + -1j)' equal to zero and attempt to solve: Simplifying -2 + -1j = 0 Solving -2 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1j = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1j = 0 + 2 -1j = 0 + 2 Combine like terms: 0 + 2 = 2 -1j = 2 Divide each side by '-1'. j = -2 Simplifying j = -2Subproblem 2
Set the factor '(9 + -1j)' equal to zero and attempt to solve: Simplifying 9 + -1j = 0 Solving 9 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1j = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1j = 0 + -9 -1j = 0 + -9 Combine like terms: 0 + -9 = -9 -1j = -9 Divide each side by '-1'. j = 9 Simplifying j = 9Solution
j = {-2, 9}
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