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Simplifying 5[i + 2] + -9 = -17 + -1i Reorder the terms: 5[2 + i] + -9 = -17 + -1i [2 * 5 + i * 5] + -9 = -17 + -1i [10 + 5i] + -9 = -17 + -1i Reorder the terms: 10 + -9 + 5i = -17 + -1i Combine like terms: 10 + -9 = 1 1 + 5i = -17 + -1i Solving 1 + 5i = -17 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 1 + 5i + i = -17 + -1i + i Combine like terms: 5i + i = 6i 1 + 6i = -17 + -1i + i Combine like terms: -1i + i = 0 1 + 6i = -17 + 0 1 + 6i = -17 Add '-1' to each side of the equation. 1 + -1 + 6i = -17 + -1 Combine like terms: 1 + -1 = 0 0 + 6i = -17 + -1 6i = -17 + -1 Combine like terms: -17 + -1 = -18 6i = -18 Divide each side by '6'. i = -3 Simplifying i = -3
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