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Simplifying j2 = 30 + -7j Solving j2 = 30 + -7j Solving for variable 'j'. Reorder the terms: -30 + 7j + j2 = 30 + -7j + -30 + 7j Reorder the terms: -30 + 7j + j2 = 30 + -30 + -7j + 7j Combine like terms: 30 + -30 = 0 -30 + 7j + j2 = 0 + -7j + 7j -30 + 7j + j2 = -7j + 7j Combine like terms: -7j + 7j = 0 -30 + 7j + j2 = 0 Factor a trinomial. (-10 + -1j)(3 + -1j) = 0Subproblem 1
Set the factor '(-10 + -1j)' equal to zero and attempt to solve: Simplifying -10 + -1j = 0 Solving -10 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1j = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1j = 0 + 10 -1j = 0 + 10 Combine like terms: 0 + 10 = 10 -1j = 10 Divide each side by '-1'. j = -10 Simplifying j = -10Subproblem 2
Set the factor '(3 + -1j)' equal to zero and attempt to solve: Simplifying 3 + -1j = 0 Solving 3 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1j = 0 + -3 -1j = 0 + -3 Combine like terms: 0 + -3 = -3 -1j = -3 Divide each side by '-1'. j = 3 Simplifying j = 3Solution
j = {-10, 3}
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