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Simplifying (sqrt(-1) + -1z)(1 + 2sqrt(-1)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Reorder the terms for easier multiplication: (-1qrst + -1z)(1 + 2sqrt(-1)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Reorder the terms for easier multiplication: (-1qrst + -1z)(1 + 2 * -1qrst) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Multiply 2 * -1 (-1qrst + -1z)(1 + -2qrst) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Multiply (-1qrst + -1z) * (1 + -2qrst) (-1qrst * (1 + -2qrst) + -1z * (1 + -2qrst)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 ((1 * -1qrst + -2qrst * -1qrst) + -1z * (1 + -2qrst)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 ((-1qrst + 2q2r2s2t2) + -1z * (1 + -2qrst)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 (-1qrst + 2q2r2s2t2 + (1 * -1z + -2qrst * -1z)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Reorder the terms: (-1qrst + 2q2r2s2t2 + (2qrstz + -1z)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 (-1qrst + 2q2r2s2t2 + (2qrstz + -1z)) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Reorder the terms: (-1qrst + 2qrstz + 2q2r2s2t2 + -1z) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 (-1qrst + 2qrstz + 2q2r2s2t2 + -1z) + (1 + -1zi)(3 + -4sqrt(-1)) + -1 + -7sqrt(-1) = 0 Reorder the terms for easier multiplication: -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (1 + -1iz)(3 + -4 * -1qrst) + -1 + -7sqrt(-1) = 0 Multiply -4 * -1 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (1 + -1iz)(3 + 4qrst) + -1 + -7sqrt(-1) = 0 Multiply (1 + -1iz) * (3 + 4qrst) -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (1(3 + 4qrst) + -1iz * (3 + 4qrst)) + -1 + -7sqrt(-1) = 0 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + ((3 * 1 + 4qrst * 1) + -1iz * (3 + 4qrst)) + -1 + -7sqrt(-1) = 0 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + ((3 + 4qrst) + -1iz * (3 + 4qrst)) + -1 + -7sqrt(-1) = 0 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (3 + 4qrst + (3 * -1iz + 4qrst * -1iz)) + -1 + -7sqrt(-1) = 0 Reorder the terms: -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (3 + 4qrst + (-4iqrstz + -3iz)) + -1 + -7sqrt(-1) = 0 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (3 + 4qrst + (-4iqrstz + -3iz)) + -1 + -7sqrt(-1) = 0 Reorder the terms: -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (3 + -4iqrstz + -3iz + 4qrst) + -1 + -7sqrt(-1) = 0 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + (3 + -4iqrstz + -3iz + 4qrst) + -1 + -7sqrt(-1) = 0 Reorder the terms for easier multiplication: -1qrst + 2qrstz + 2q2r2s2t2 + -1z + 3 + -4iqrstz + -3iz + 4qrst + -1 + -7 * -1qrst = 0 Multiply -7 * -1 -1qrst + 2qrstz + 2q2r2s2t2 + -1z + 3 + -4iqrstz + -3iz + 4qrst + -1 + 7qrst = 0 Reorder the terms: 3 + -1 + -4iqrstz + -3iz + -1qrst + 4qrst + 7qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 Combine like terms: 3 + -1 = 2 2 + -4iqrstz + -3iz + -1qrst + 4qrst + 7qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 Combine like terms: -1qrst + 4qrst = 3qrst 2 + -4iqrstz + -3iz + 3qrst + 7qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 Combine like terms: 3qrst + 7qrst = 10qrst 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 Solving 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -2 + -1z = 0 + -2 Reorder the terms: 2 + -2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -2 -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2 Add '-10qrst' to each side of the equation. -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -10qrst + -1z = -2 + -10qrst Reorder the terms: -4iqrstz + -3iz + 10qrst + -10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2 + -10qrst Combine like terms: 10qrst + -10qrst = 0 -4iqrstz + -3iz + 0 + 2qrstz + 2q2r2s2t2 + -1z = -2 + -10qrst -4iqrstz + -3iz + 2qrstz + 2q2r2s2t2 + -1z = -2 + -10qrst Add '-2qrstz' to each side of the equation. -4iqrstz + -3iz + 2qrstz + 2q2r2s2t2 + -2qrstz + -1z = -2 + -10qrst + -2qrstz Reorder the terms: -4iqrstz + -3iz + 2qrstz + -2qrstz + 2q2r2s2t2 + -1z = -2 + -10qrst + -2qrstz Combine like terms: 2qrstz + -2qrstz = 0 -4iqrstz + -3iz + 0 + 2q2r2s2t2 + -1z = -2 + -10qrst + -2qrstz -4iqrstz + -3iz + 2q2r2s2t2 + -1z = -2 + -10qrst + -2qrstz Add '-2q2r2s2t2' to each side of the equation. -4iqrstz + -3iz + 2q2r2s2t2 + -2q2r2s2t2 + -1z = -2 + -10qrst + -2qrstz + -2q2r2s2t2 Combine like terms: 2q2r2s2t2 + -2q2r2s2t2 = 0 -4iqrstz + -3iz + 0 + -1z = -2 + -10qrst + -2qrstz + -2q2r2s2t2 -4iqrstz + -3iz + -1z = -2 + -10qrst + -2qrstz + -2q2r2s2t2 Add 'z' to each side of the equation. -4iqrstz + -3iz + -1z + z = -2 + -10qrst + -2qrstz + -2q2r2s2t2 + z Combine like terms: -1z + z = 0 -4iqrstz + -3iz + 0 = -2 + -10qrst + -2qrstz + -2q2r2s2t2 + z -4iqrstz + -3iz = -2 + -10qrst + -2qrstz + -2q2r2s2t2 + z Reorder the terms: 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2 + -10qrst + -2qrstz + -2q2r2s2t2 + z + 2 + 10qrst + 2qrstz + 2q2r2s2t2 + -1z Reorder the terms: 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2 + 2 + -10qrst + 10qrst + -2qrstz + 2qrstz + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z Combine like terms: -2 + 2 = 0 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -10qrst + 10qrst + -2qrstz + 2qrstz + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -10qrst + 10qrst + -2qrstz + 2qrstz + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z Combine like terms: -10qrst + 10qrst = 0 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -2qrstz + 2qrstz + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2qrstz + 2qrstz + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z Combine like terms: -2qrstz + 2qrstz = 0 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + -2q2r2s2t2 + 2q2r2s2t2 + z + -1z 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = -2q2r2s2t2 + 2q2r2s2t2 + z + -1z Combine like terms: -2q2r2s2t2 + 2q2r2s2t2 = 0 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 + z + -1z 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = z + -1z Combine like terms: z + -1z = 0 2 + -4iqrstz + -3iz + 10qrst + 2qrstz + 2q2r2s2t2 + -1z = 0 The solution to this equation could not be determined.
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