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Simplifying j2 + -8j = -7 Reorder the terms: -8j + j2 = -7 Solving -8j + j2 = -7 Solving for variable 'j'. Reorder the terms: 7 + -8j + j2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -8j + j2 = 0 Factor a trinomial. (1 + -1j)(7 + -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 '(7 + -1j)' equal to zero and attempt to solve: Simplifying 7 + -1j = 0 Solving 7 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1j = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1j = 0 + -7 -1j = 0 + -7 Combine like terms: 0 + -7 = -7 -1j = -7 Divide each side by '-1'. j = 7 Simplifying j = 7Solution
j = {1, 7}
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