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Simplifying (3 + 2i) + (1 + -4i) = 0 Remove parenthesis around (3 + 2i) 3 + 2i + (1 + -4i) = 0 Remove parenthesis around (1 + -4i) 3 + 2i + 1 + -4i = 0 Reorder the terms: 3 + 1 + 2i + -4i = 0 Combine like terms: 3 + 1 = 4 4 + 2i + -4i = 0 Combine like terms: 2i + -4i = -2i 4 + -2i = 0 Solving 4 + -2i = 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 + -2i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2i = 0 + -4 -2i = 0 + -4 Combine like terms: 0 + -4 = -4 -2i = -4 Divide each side by '-2'. i = 2 Simplifying i = 2
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