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Simplifying 3(j + 5) = 8(11 + -1j) Reorder the terms: 3(5 + j) = 8(11 + -1j) (5 * 3 + j * 3) = 8(11 + -1j) (15 + 3j) = 8(11 + -1j) 15 + 3j = (11 * 8 + -1j * 8) 15 + 3j = (88 + -8j) Solving 15 + 3j = 88 + -8j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '8j' to each side of the equation. 15 + 3j + 8j = 88 + -8j + 8j Combine like terms: 3j + 8j = 11j 15 + 11j = 88 + -8j + 8j Combine like terms: -8j + 8j = 0 15 + 11j = 88 + 0 15 + 11j = 88 Add '-15' to each side of the equation. 15 + -15 + 11j = 88 + -15 Combine like terms: 15 + -15 = 0 0 + 11j = 88 + -15 11j = 88 + -15 Combine like terms: 88 + -15 = 73 11j = 73 Divide each side by '11'. j = 6.636363636 Simplifying j = 6.636363636
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