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Simplifying (3 + -2i) + -1(-4 + -3i) = 0 Remove parenthesis around (3 + -2i) 3 + -2i + -1(-4 + -3i) = 0 3 + -2i + (-4 * -1 + -3i * -1) = 0 3 + -2i + (4 + 3i) = 0 Reorder the terms: 3 + 4 + -2i + 3i = 0 Combine like terms: 3 + 4 = 7 7 + -2i + 3i = 0 Combine like terms: -2i + 3i = 1i 7 + 1i = 0 Solving 7 + 1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 1i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 1i = 0 + -7 1i = 0 + -7 Combine like terms: 0 + -7 = -7 1i = -7 Divide each side by '1'. i = -7 Simplifying i = -7
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