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Simplifying (12 + 5i) + -1(8 + i) = 0 Remove parenthesis around (12 + 5i) 12 + 5i + -1(8 + i) = 0 12 + 5i + (8 * -1 + i * -1) = 0 12 + 5i + (-8 + -1i) = 0 Reorder the terms: 12 + -8 + 5i + -1i = 0 Combine like terms: 12 + -8 = 4 4 + 5i + -1i = 0 Combine like terms: 5i + -1i = 4i 4 + 4i = 0 Solving 4 + 4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 4i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4i = 0 + -4 4i = 0 + -4 Combine like terms: 0 + -4 = -4 4i = -4 Divide each side by '4'. i = -1 Simplifying i = -1
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