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Simplifying 7 + -1(-9 + 2i) + -1(-17 + -1i) = 0 7 + (-9 * -1 + 2i * -1) + -1(-17 + -1i) = 0 7 + (9 + -2i) + -1(-17 + -1i) = 0 7 + 9 + -2i + (-17 * -1 + -1i * -1) = 0 7 + 9 + -2i + (17 + 1i) = 0 Reorder the terms: 7 + 9 + 17 + -2i + 1i = 0 Combine like terms: 7 + 9 = 16 16 + 17 + -2i + 1i = 0 Combine like terms: 16 + 17 = 33 33 + -2i + 1i = 0 Combine like terms: -2i + 1i = -1i 33 + -1i = 0 Solving 33 + -1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1i = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1i = 0 + -33 -1i = 0 + -33 Combine like terms: 0 + -33 = -33 -1i = -33 Divide each side by '-1'. i = 33 Simplifying i = 33
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