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Simplifying (14 + 3i) + -1(-12 + -7i) + -1(6 + 2i) = 0 Remove parenthesis around (14 + 3i) 14 + 3i + -1(-12 + -7i) + -1(6 + 2i) = 0 14 + 3i + (-12 * -1 + -7i * -1) + -1(6 + 2i) = 0 14 + 3i + (12 + 7i) + -1(6 + 2i) = 0 14 + 3i + 12 + 7i + (6 * -1 + 2i * -1) = 0 14 + 3i + 12 + 7i + (-6 + -2i) = 0 Reorder the terms: 14 + 12 + -6 + 3i + 7i + -2i = 0 Combine like terms: 14 + 12 = 26 26 + -6 + 3i + 7i + -2i = 0 Combine like terms: 26 + -6 = 20 20 + 3i + 7i + -2i = 0 Combine like terms: 3i + 7i = 10i 20 + 10i + -2i = 0 Combine like terms: 10i + -2i = 8i 20 + 8i = 0 Solving 20 + 8i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + 8i = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 8i = 0 + -20 8i = 0 + -20 Combine like terms: 0 + -20 = -20 8i = -20 Divide each side by '8'. i = -2.5 Simplifying i = -2.5
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