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Simplifying (x + 1)(x + -1(1 + i))(x + -1(1 + -1i)) = 0 Reorder the terms: (1 + x)(x + -1(1 + i))(x + -1(1 + -1i)) = 0 (1 + x)(x + (1 * -1 + i * -1))(x + -1(1 + -1i)) = 0 (1 + x)(x + (-1 + -1i))(x + -1(1 + -1i)) = 0 Reorder the terms: (1 + x)(-1 + -1i + x)(x + -1(1 + -1i)) = 0 (1 + x)(-1 + -1i + x)(x + (1 * -1 + -1i * -1)) = 0 (1 + x)(-1 + -1i + x)(x + (-1 + 1i)) = 0 Reorder the terms: (1 + x)(-1 + -1i + x)(-1 + 1i + x) = 0 Multiply (1 + x) * (-1 + -1i + x) (1(-1 + -1i + x) + x(-1 + -1i + x))(-1 + 1i + x) = 0 ((-1 * 1 + -1i * 1 + x * 1) + x(-1 + -1i + x))(-1 + 1i + x) = 0 ((-1 + -1i + 1x) + x(-1 + -1i + x))(-1 + 1i + x) = 0 (-1 + -1i + 1x + (-1 * x + -1i * x + x * x))(-1 + 1i + x) = 0 Reorder the terms: (-1 + -1i + 1x + (-1ix + -1x + x2))(-1 + 1i + x) = 0 (-1 + -1i + 1x + (-1ix + -1x + x2))(-1 + 1i + x) = 0 Reorder the terms: (-1 + -1i + -1ix + 1x + -1x + x2)(-1 + 1i + x) = 0 Combine like terms: 1x + -1x = 0 (-1 + -1i + -1ix + 0 + x2)(-1 + 1i + x) = 0 (-1 + -1i + -1ix + x2)(-1 + 1i + x) = 0 Multiply (-1 + -1i + -1ix + x2) * (-1 + 1i + x) (-1(-1 + 1i + x) + -1i * (-1 + 1i + x) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 ((-1 * -1 + 1i * -1 + x * -1) + -1i * (-1 + 1i + x) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 ((1 + -1i + -1x) + -1i * (-1 + 1i + x) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 (1 + -1i + -1x + (-1 * -1i + 1i * -1i + x * -1i) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 Reorder the terms: (1 + -1i + -1x + (1i + -1ix + -1i2) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 (1 + -1i + -1x + (1i + -1ix + -1i2) + -1ix * (-1 + 1i + x) + x2(-1 + 1i + x)) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + (-1 * -1ix + 1i * -1ix + x * -1ix) + x2(-1 + 1i + x)) = 0 Reorder the terms: (1 + -1i + -1x + 1i + -1ix + -1i2 + (1ix + -1ix2 + -1i2x) + x2(-1 + 1i + x)) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + (1ix + -1ix2 + -1i2x) + x2(-1 + 1i + x)) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + 1ix + -1ix2 + -1i2x + (-1 * x2 + 1i * x2 + x * x2)) = 0 Reorder the terms: (1 + -1i + -1x + 1i + -1ix + -1i2 + 1ix + -1ix2 + -1i2x + (1ix2 + -1x2 + x3)) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + 1ix + -1ix2 + -1i2x + (1ix2 + -1x2 + x3)) = 0 Reorder the terms: (1 + -1i + 1i + -1ix + 1ix + -1ix2 + 1ix2 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 Combine like terms: -1i + 1i = 0 (1 + 0 + -1ix + 1ix + -1ix2 + 1ix2 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 (1 + -1ix + 1ix + -1ix2 + 1ix2 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 Combine like terms: -1ix + 1ix = 0 (1 + 0 + -1ix2 + 1ix2 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 (1 + -1ix2 + 1ix2 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 Combine like terms: -1ix2 + 1ix2 = 0 (1 + 0 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 (1 + -1i2 + -1i2x + -1x + -1x2 + x3) = 0 Solving 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1i2 + -1i2x + -1x + -1x2 + -1 + x3 = 0 + -1 Reorder the terms: 1 + -1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + -1 -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1i2 + -1i2x + -1x + -1x2 + x3 = -1 Add 'x' to each side of the equation. -1i2 + -1i2x + -1x + -1x2 + x + x3 = -1 + x Reorder the terms: -1i2 + -1i2x + -1x + x + -1x2 + x3 = -1 + x Combine like terms: -1x + x = 0 -1i2 + -1i2x + 0 + -1x2 + x3 = -1 + x -1i2 + -1i2x + -1x2 + x3 = -1 + x Add 'x2' to each side of the equation. -1i2 + -1i2x + -1x2 + x2 + x3 = -1 + x + x2 Combine like terms: -1x2 + x2 = 0 -1i2 + -1i2x + 0 + x3 = -1 + x + x2 -1i2 + -1i2x + x3 = -1 + x + x2 Add '-1x3' to each side of the equation. -1i2 + -1i2x + x3 + -1x3 = -1 + x + x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -1i2 + -1i2x + 0 = -1 + x + x2 + -1x3 -1i2 + -1i2x = -1 + x + x2 + -1x3 Reorder the terms: 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = -1 + x + x2 + -1x3 + 1 + -1x + -1x2 + x3 Reorder the terms: 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = -1 + 1 + x + -1x + x2 + -1x2 + -1x3 + x3 Combine like terms: -1 + 1 = 0 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + x + -1x + x2 + -1x2 + -1x3 + x3 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = x + -1x + x2 + -1x2 + -1x3 + x3 Combine like terms: x + -1x = 0 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + x2 + -1x2 + -1x3 + x3 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = x2 + -1x2 + -1x3 + x3 Combine like terms: x2 + -1x2 = 0 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 + -1x3 + x3 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 1 + -1i2 + -1i2x + -1x + -1x2 + x3 = 0 The solution to this equation could not be determined.
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