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Simplifying 3(j + 5) = 5(11 + -1j) Reorder the terms: 3(5 + j) = 5(11 + -1j) (5 * 3 + j * 3) = 5(11 + -1j) (15 + 3j) = 5(11 + -1j) 15 + 3j = (11 * 5 + -1j * 5) 15 + 3j = (55 + -5j) Solving 15 + 3j = 55 + -5j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5j' to each side of the equation. 15 + 3j + 5j = 55 + -5j + 5j Combine like terms: 3j + 5j = 8j 15 + 8j = 55 + -5j + 5j Combine like terms: -5j + 5j = 0 15 + 8j = 55 + 0 15 + 8j = 55 Add '-15' to each side of the equation. 15 + -15 + 8j = 55 + -15 Combine like terms: 15 + -15 = 0 0 + 8j = 55 + -15 8j = 55 + -15 Combine like terms: 55 + -15 = 40 8j = 40 Divide each side by '8'. j = 5 Simplifying j = 5
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