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Simplifying (12 + 3i) + -1(3 + -1i) = 0 Remove parenthesis around (12 + 3i) 12 + 3i + -1(3 + -1i) = 0 12 + 3i + (3 * -1 + -1i * -1) = 0 12 + 3i + (-3 + 1i) = 0 Reorder the terms: 12 + -3 + 3i + 1i = 0 Combine like terms: 12 + -3 = 9 9 + 3i + 1i = 0 Combine like terms: 3i + 1i = 4i 9 + 4i = 0 Solving 9 + 4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4i = 0 + -9 4i = 0 + -9 Combine like terms: 0 + -9 = -9 4i = -9 Divide each side by '4'. i = -2.25 Simplifying i = -2.25
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