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Simplifying (8j + -7)(j + 4) = 0 Reorder the terms: (-7 + 8j)(j + 4) = 0 Reorder the terms: (-7 + 8j)(4 + j) = 0 Multiply (-7 + 8j) * (4 + j) (-7(4 + j) + 8j * (4 + j)) = 0 ((4 * -7 + j * -7) + 8j * (4 + j)) = 0 ((-28 + -7j) + 8j * (4 + j)) = 0 (-28 + -7j + (4 * 8j + j * 8j)) = 0 (-28 + -7j + (32j + 8j2)) = 0 Combine like terms: -7j + 32j = 25j (-28 + 25j + 8j2) = 0 Solving -28 + 25j + 8j2 = 0 Solving for variable 'j'. Factor a trinomial. (-4 + -1j)(7 + -8j) = 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 + -8j)' equal to zero and attempt to solve: Simplifying 7 + -8j = 0 Solving 7 + -8j = 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 + -8j = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8j = 0 + -7 -8j = 0 + -7 Combine like terms: 0 + -7 = -7 -8j = -7 Divide each side by '-8'. j = 0.875 Simplifying j = 0.875Solution
j = {-4, 0.875}
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