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Simplifying (x + -1)(x + -1(2 + i))(x + -1(2 + -1i)) = 0 Reorder the terms: (-1 + x)(x + -1(2 + i))(x + -1(2 + -1i)) = 0 (-1 + x)(x + (2 * -1 + i * -1))(x + -1(2 + -1i)) = 0 (-1 + x)(x + (-2 + -1i))(x + -1(2 + -1i)) = 0 Reorder the terms: (-1 + x)(-2 + -1i + x)(x + -1(2 + -1i)) = 0 (-1 + x)(-2 + -1i + x)(x + (2 * -1 + -1i * -1)) = 0 (-1 + x)(-2 + -1i + x)(x + (-2 + 1i)) = 0 Reorder the terms: (-1 + x)(-2 + -1i + x)(-2 + 1i + x) = 0 Multiply (-1 + x) * (-2 + -1i + x) (-1(-2 + -1i + x) + x(-2 + -1i + x))(-2 + 1i + x) = 0 ((-2 * -1 + -1i * -1 + x * -1) + x(-2 + -1i + x))(-2 + 1i + x) = 0 ((2 + 1i + -1x) + x(-2 + -1i + x))(-2 + 1i + x) = 0 (2 + 1i + -1x + (-2 * x + -1i * x + x * x))(-2 + 1i + x) = 0 Reorder the terms: (2 + 1i + -1x + (-1ix + -2x + x2))(-2 + 1i + x) = 0 (2 + 1i + -1x + (-1ix + -2x + x2))(-2 + 1i + x) = 0 Reorder the terms: (2 + 1i + -1ix + -1x + -2x + x2)(-2 + 1i + x) = 0 Combine like terms: -1x + -2x = -3x (2 + 1i + -1ix + -3x + x2)(-2 + 1i + x) = 0 Multiply (2 + 1i + -1ix + -3x + x2) * (-2 + 1i + x) (2(-2 + 1i + x) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 ((-2 * 2 + 1i * 2 + x * 2) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 ((-4 + 2i + 2x) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + (-2 * 1i + 1i * 1i + x * 1i) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 Reorder the terms: (-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + (-2 * -1ix + 1i * -1ix + x * -1ix) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 Reorder the terms: (-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-2 * -3x + 1i * -3x + x * -3x) + x2(-2 + 1i + x)) = 0 Reorder the terms: (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + 1i + x)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (-2 * x2 + 1i * x2 + x * x2)) = 0 Reorder the terms: (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (1ix2 + -2x2 + x3)) = 0 (-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (1ix2 + -2x2 + x3)) = 0 Reorder the terms: (-4 + 2i + -2i + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 2i + -2i = 0 (-4 + 0 + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 (-4 + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 1ix + 2ix = 3ix (-4 + 3ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 3ix + -3ix = 0 (-4 + 0 + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 (-4 + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: -1ix2 + 1ix2 = 0 (-4 + 0 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 (-4 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 2x + 6x = 8x (-4 + 1i2 + -1i2x + 8x + -3x2 + -2x2 + x3) = 0 Combine like terms: -3x2 + -2x2 = -5x2 (-4 + 1i2 + -1i2x + 8x + -5x2 + x3) = 0 Solving -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 1i2 + -1i2x + 8x + -5x2 + 4 + x3 = 0 + 4 Reorder the terms: -4 + 4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 Combine like terms: 0 + 4 = 4 1i2 + -1i2x + 8x + -5x2 + x3 = 4 Add '-8x' to each side of the equation. 1i2 + -1i2x + 8x + -5x2 + -8x + x3 = 4 + -8x Reorder the terms: 1i2 + -1i2x + 8x + -8x + -5x2 + x3 = 4 + -8x Combine like terms: 8x + -8x = 0 1i2 + -1i2x + 0 + -5x2 + x3 = 4 + -8x 1i2 + -1i2x + -5x2 + x3 = 4 + -8x Add '5x2' to each side of the equation. 1i2 + -1i2x + -5x2 + 5x2 + x3 = 4 + -8x + 5x2 Combine like terms: -5x2 + 5x2 = 0 1i2 + -1i2x + 0 + x3 = 4 + -8x + 5x2 1i2 + -1i2x + x3 = 4 + -8x + 5x2 Add '-1x3' to each side of the equation. 1i2 + -1i2x + x3 + -1x3 = 4 + -8x + 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 1i2 + -1i2x + 0 = 4 + -8x + 5x2 + -1x3 1i2 + -1i2x = 4 + -8x + 5x2 + -1x3 Reorder the terms: -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 4 + -8x + 5x2 + -1x3 + -4 + 8x + -5x2 + x3 Reorder the terms: -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 4 + -4 + -8x + 8x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: 4 + -4 = 0 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + -8x + 8x + 5x2 + -5x2 + -1x3 + x3 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = -8x + 8x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: -8x + 8x = 0 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 5x2 + -5x2 + -1x3 + x3 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3 Combine like terms: 5x2 + -5x2 = 0 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + -1x3 + x3 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 The solution to this equation could not be determined.
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