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Simplifying 3i + 2k + -1i + k = 0 Reorder the terms: 3i + -1i + 2k + k = 0 Combine like terms: 3i + -1i = 2i 2i + 2k + k = 0 Combine like terms: 2k + k = 3k 2i + 3k = 0 Solving 2i + 3k = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3k' to each side of the equation. 2i + 3k + -3k = 0 + -3k Combine like terms: 3k + -3k = 0 2i + 0 = 0 + -3k 2i = 0 + -3k Remove the zero: 2i = -3k Divide each side by '2'. i = -1.5k Simplifying i = -1.5k
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