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