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Simplifying 4(2 + j) + -3(6 + 2j) + 7j = 0 (2 * 4 + j * 4) + -3(6 + 2j) + 7j = 0 (8 + 4j) + -3(6 + 2j) + 7j = 0 8 + 4j + (6 * -3 + 2j * -3) + 7j = 0 8 + 4j + (-18 + -6j) + 7j = 0 Reorder the terms: 8 + -18 + 4j + -6j + 7j = 0 Combine like terms: 8 + -18 = -10 -10 + 4j + -6j + 7j = 0 Combine like terms: 4j + -6j = -2j -10 + -2j + 7j = 0 Combine like terms: -2j + 7j = 5j -10 + 5j = 0 Solving -10 + 5j = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 5j = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 5j = 0 + 10 5j = 0 + 10 Combine like terms: 0 + 10 = 10 5j = 10 Divide each side by '5'. j = 2 Simplifying j = 2
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