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Simplifying 5(-2j + 8) + 4(6 + -3j) = 0 Reorder the terms: 5(8 + -2j) + 4(6 + -3j) = 0 (8 * 5 + -2j * 5) + 4(6 + -3j) = 0 (40 + -10j) + 4(6 + -3j) = 0 40 + -10j + (6 * 4 + -3j * 4) = 0 40 + -10j + (24 + -12j) = 0 Reorder the terms: 40 + 24 + -10j + -12j = 0 Combine like terms: 40 + 24 = 64 64 + -10j + -12j = 0 Combine like terms: -10j + -12j = -22j 64 + -22j = 0 Solving 64 + -22j = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + -22j = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -22j = 0 + -64 -22j = 0 + -64 Combine like terms: 0 + -64 = -64 -22j = -64 Divide each side by '-22'. j = 2.909090909 Simplifying j = 2.909090909
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