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Simplifying In(5 + 8i) = 0 (5 * nI + 8i * nI) = 0 Reorder the terms: (8inI + 5nI) = 0 (8inI + 5nI) = 0 Solving 8inI + 5nI = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5nI' to each side of the equation. 8inI + 5nI + -5nI = 0 + -5nI Combine like terms: 5nI + -5nI = 0 8inI + 0 = 0 + -5nI 8inI = 0 + -5nI Remove the zero: 8inI = -5nI Divide each side by '8nI'. i = -0.625 Simplifying i = -0.625
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