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Simplifying 5(3 + -1j) + 8j = j + -1 (3 * 5 + -1j * 5) + 8j = j + -1 (15 + -5j) + 8j = j + -1 Combine like terms: -5j + 8j = 3j 15 + 3j = j + -1 Reorder the terms: 15 + 3j = -1 + j Solving 15 + 3j = -1 + j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1j' to each side of the equation. 15 + 3j + -1j = -1 + j + -1j Combine like terms: 3j + -1j = 2j 15 + 2j = -1 + j + -1j Combine like terms: j + -1j = 0 15 + 2j = -1 + 0 15 + 2j = -1 Add '-15' to each side of the equation. 15 + -15 + 2j = -1 + -15 Combine like terms: 15 + -15 = 0 0 + 2j = -1 + -15 2j = -1 + -15 Combine like terms: -1 + -15 = -16 2j = -16 Divide each side by '2'. j = -8 Simplifying j = -8
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