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Simplifying 0 = (4 + i) + -1(-8 + -3i) Remove parenthesis around (4 + i) 0 = 4 + i + -1(-8 + -3i) 0 = 4 + i + (-8 * -1 + -3i * -1) 0 = 4 + i + (8 + 3i) Reorder the terms: 0 = 4 + 8 + i + 3i Combine like terms: 4 + 8 = 12 0 = 12 + i + 3i Combine like terms: i + 3i = 4i 0 = 12 + 4i Solving 0 = 12 + 4i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4i' to each side of the equation. 0 + -4i = 12 + 4i + -4i Remove the zero: -4i = 12 + 4i + -4i Combine like terms: 4i + -4i = 0 -4i = 12 + 0 -4i = 12 Divide each side by '-4'. i = -3 Simplifying i = -3
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