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