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