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Simplifying (3 + -1i) + -1(4 + 3i) + (1 + -2i) = 0 Remove parenthesis around (3 + -1i) 3 + -1i + -1(4 + 3i) + (1 + -2i) = 0 3 + -1i + (4 * -1 + 3i * -1) + (1 + -2i) = 0 3 + -1i + (-4 + -3i) + (1 + -2i) = 0 Remove parenthesis around (1 + -2i) 3 + -1i + -4 + -3i + 1 + -2i = 0 Reorder the terms: 3 + -4 + 1 + -1i + -3i + -2i = 0 Combine like terms: 3 + -4 = -1 -1 + 1 + -1i + -3i + -2i = 0 Combine like terms: -1 + 1 = 0 0 + -1i + -3i + -2i = 0 -1i + -3i + -2i = 0 Combine like terms: -1i + -3i = -4i -4i + -2i = 0 Combine like terms: -4i + -2i = -6i -6i = 0 Solving -6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Divide each side by '-6'. i = 0 Simplifying i = 0
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