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Simplifying 3j + -2k + -3(5 + -1j) = 0 3j + -2k + (5 * -3 + -1j * -3) = 0 3j + -2k + (-15 + 3j) = 0 Reorder the terms: -15 + 3j + 3j + -2k = 0 Combine like terms: 3j + 3j = 6j -15 + 6j + -2k = 0 Solving -15 + 6j + -2k = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 6j + 15 + -2k = 0 + 15 Reorder the terms: -15 + 15 + 6j + -2k = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6j + -2k = 0 + 15 6j + -2k = 0 + 15 Combine like terms: 0 + 15 = 15 6j + -2k = 15 Add '2k' to each side of the equation. 6j + -2k + 2k = 15 + 2k Combine like terms: -2k + 2k = 0 6j + 0 = 15 + 2k 6j = 15 + 2k Divide each side by '6'. j = 2.5 + 0.3333333333k Simplifying j = 2.5 + 0.3333333333k
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