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Simplifying (4 + i) + -1(2 + 3i) = 0 Remove parenthesis around (4 + i) 4 + i + -1(2 + 3i) = 0 4 + i + (2 * -1 + 3i * -1) = 0 4 + i + (-2 + -3i) = 0 Reorder the terms: 4 + -2 + i + -3i = 0 Combine like terms: 4 + -2 = 2 2 + i + -3i = 0 Combine like terms: i + -3i = -2i 2 + -2i = 0 Solving 2 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -2i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2i = 0 + -2 -2i = 0 + -2 Combine like terms: 0 + -2 = -2 -2i = -2 Divide each side by '-2'. i = 1 Simplifying i = 1
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