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Simplifying (7 + j)(4 + -1j) = 0 Multiply (7 + j) * (4 + -1j) (7(4 + -1j) + j(4 + -1j)) = 0 ((4 * 7 + -1j * 7) + j(4 + -1j)) = 0 ((28 + -7j) + j(4 + -1j)) = 0 (28 + -7j + (4 * j + -1j * j)) = 0 (28 + -7j + (4j + -1j2)) = 0 Combine like terms: -7j + 4j = -3j (28 + -3j + -1j2) = 0 Solving 28 + -3j + -1j2 = 0 Solving for variable 'j'. Factor a trinomial. (4 + -1j)(7 + j) = 0Subproblem 1
Set the factor '(4 + -1j)' equal to zero and attempt to solve: Simplifying 4 + -1j = 0 Solving 4 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1j = 0 + -4 -1j = 0 + -4 Combine like terms: 0 + -4 = -4 -1j = -4 Divide each side by '-1'. j = 4 Simplifying j = 4Subproblem 2
Set the factor '(7 + j)' equal to zero and attempt to solve: Simplifying 7 + j = 0 Solving 7 + j = 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 + j = 0 + -7 Combine like terms: 7 + -7 = 0 0 + j = 0 + -7 j = 0 + -7 Combine like terms: 0 + -7 = -7 j = -7 Simplifying j = -7Solution
j = {4, -7}
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