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Simplifying (3 + -1i) + (1 + -2i) = 0 Remove parenthesis around (3 + -1i) 3 + -1i + (1 + -2i) = 0 Remove parenthesis around (1 + -2i) 3 + -1i + 1 + -2i = 0 Reorder the terms: 3 + 1 + -1i + -2i = 0 Combine like terms: 3 + 1 = 4 4 + -1i + -2i = 0 Combine like terms: -1i + -2i = -3i 4 + -3i = 0 Solving 4 + -3i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333
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