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Simplifying 4j + 5(1 + -1j) = 6j + 3(1 + -1j) 4j + (1 * 5 + -1j * 5) = 6j + 3(1 + -1j) 4j + (5 + -5j) = 6j + 3(1 + -1j) Reorder the terms: 5 + 4j + -5j = 6j + 3(1 + -1j) Combine like terms: 4j + -5j = -1j 5 + -1j = 6j + 3(1 + -1j) 5 + -1j = 6j + (1 * 3 + -1j * 3) 5 + -1j = 6j + (3 + -3j) Reorder the terms: 5 + -1j = 3 + 6j + -3j Combine like terms: 6j + -3j = 3j 5 + -1j = 3 + 3j Solving 5 + -1j = 3 + 3j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3j' to each side of the equation. 5 + -1j + -3j = 3 + 3j + -3j Combine like terms: -1j + -3j = -4j 5 + -4j = 3 + 3j + -3j Combine like terms: 3j + -3j = 0 5 + -4j = 3 + 0 5 + -4j = 3 Add '-5' to each side of the equation. 5 + -5 + -4j = 3 + -5 Combine like terms: 5 + -5 = 0 0 + -4j = 3 + -5 -4j = 3 + -5 Combine like terms: 3 + -5 = -2 -4j = -2 Divide each side by '-4'. j = 0.5 Simplifying j = 0.5
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