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Simplifying 0 = j2 + -9j + 8 Reorder the terms: 0 = 8 + -9j + j2 Solving 0 = 8 + -9j + j2 Solving for variable 'j'. Combine like terms: 0 + -8 = -8 -8 + 9j + -1j2 = 8 + -9j + j2 + -8 + 9j + -1j2 Reorder the terms: -8 + 9j + -1j2 = 8 + -8 + -9j + 9j + j2 + -1j2 Combine like terms: 8 + -8 = 0 -8 + 9j + -1j2 = 0 + -9j + 9j + j2 + -1j2 -8 + 9j + -1j2 = -9j + 9j + j2 + -1j2 Combine like terms: -9j + 9j = 0 -8 + 9j + -1j2 = 0 + j2 + -1j2 -8 + 9j + -1j2 = j2 + -1j2 Combine like terms: j2 + -1j2 = 0 -8 + 9j + -1j2 = 0 Factor a trinomial. (-8 + j)(1 + -1j) = 0Subproblem 1
Set the factor '(-8 + j)' equal to zero and attempt to solve: Simplifying -8 + j = 0 Solving -8 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + j = 0 + 8 Combine like terms: -8 + 8 = 0 0 + j = 0 + 8 j = 0 + 8 Combine like terms: 0 + 8 = 8 j = 8 Simplifying j = 8Subproblem 2
Set the factor '(1 + -1j)' equal to zero and attempt to solve: Simplifying 1 + -1j = 0 Solving 1 + -1j = 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 + -1j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1j = 0 + -1 -1j = 0 + -1 Combine like terms: 0 + -1 = -1 -1j = -1 Divide each side by '-1'. j = 1 Simplifying j = 1Solution
j = {8, 1}
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