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Simplifying 5(7j + -3k) + -11(-1j + k) = 0 (7j * 5 + -3k * 5) + -11(-1j + k) = 0 (35j + -15k) + -11(-1j + k) = 0 35j + -15k + (-1j * -11 + k * -11) = 0 35j + -15k + (11j + -11k) = 0 Reorder the terms: 35j + 11j + -15k + -11k = 0 Combine like terms: 35j + 11j = 46j 46j + -15k + -11k = 0 Combine like terms: -15k + -11k = -26k 46j + -26k = 0 Solving 46j + -26k = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '26k' to each side of the equation. 46j + -26k + 26k = 0 + 26k Combine like terms: -26k + 26k = 0 46j + 0 = 0 + 26k 46j = 0 + 26k Remove the zero: 46j = 26k Divide each side by '46'. j = 0.5652173913k Simplifying j = 0.5652173913k
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