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Simplifying 8j(j + -1) = 5(1 + -1j) Reorder the terms: 8j(-1 + j) = 5(1 + -1j) (-1 * 8j + j * 8j) = 5(1 + -1j) (-8j + 8j2) = 5(1 + -1j) -8j + 8j2 = (1 * 5 + -1j * 5) -8j + 8j2 = (5 + -5j) Solving -8j + 8j2 = 5 + -5j Solving for variable 'j'. Reorder the terms: -5 + -8j + 5j + 8j2 = 5 + -5j + -5 + 5j Combine like terms: -8j + 5j = -3j -5 + -3j + 8j2 = 5 + -5j + -5 + 5j Reorder the terms: -5 + -3j + 8j2 = 5 + -5 + -5j + 5j Combine like terms: 5 + -5 = 0 -5 + -3j + 8j2 = 0 + -5j + 5j -5 + -3j + 8j2 = -5j + 5j Combine like terms: -5j + 5j = 0 -5 + -3j + 8j2 = 0 Factor a trinomial. (-5 + -8j)(1 + -1j) = 0Subproblem 1
Set the factor '(-5 + -8j)' equal to zero and attempt to solve: Simplifying -5 + -8j = 0 Solving -5 + -8j = 0 Move all terms containing j to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -8j = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8j = 0 + 5 -8j = 0 + 5 Combine like terms: 0 + 5 = 5 -8j = 5 Divide each side by '-8'. j = -0.625 Simplifying j = -0.625Subproblem 2
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 = 1Solution
j = {-0.625, 1}
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