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Simplifying (X + 4 + -2i)(x + 4 + 2i) = 0 Reorder the terms: (4 + X + -2i)(x + 4 + 2i) = 0 Reorder the terms: (4 + X + -2i)(4 + 2i + x) = 0 Multiply (4 + X + -2i) * (4 + 2i + x) (4(4 + 2i + x) + X(4 + 2i + x) + -2i * (4 + 2i + x)) = 0 ((4 * 4 + 2i * 4 + x * 4) + X(4 + 2i + x) + -2i * (4 + 2i + x)) = 0 ((16 + 8i + 4x) + X(4 + 2i + x) + -2i * (4 + 2i + x)) = 0 (16 + 8i + 4x + (4 * X + 2i * X + x * X) + -2i * (4 + 2i + x)) = 0 (16 + 8i + 4x + (4X + 2iX + xX) + -2i * (4 + 2i + x)) = 0 (16 + 8i + 4x + 4X + 2iX + xX + (4 * -2i + 2i * -2i + x * -2i)) = 0 Reorder the terms: (16 + 8i + 4x + 4X + 2iX + xX + (-8i + -2ix + -4i2)) = 0 (16 + 8i + 4x + 4X + 2iX + xX + (-8i + -2ix + -4i2)) = 0 Reorder the terms: (16 + 4X + 8i + -8i + 2iX + -2ix + -4i2 + 4x + xX) = 0 Combine like terms: 8i + -8i = 0 (16 + 4X + 0 + 2iX + -2ix + -4i2 + 4x + xX) = 0 (16 + 4X + 2iX + -2ix + -4i2 + 4x + xX) = 0 Solving 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + 4X + 2iX + -2ix + -4i2 + 4x + -16 + xX = 0 + -16 Reorder the terms: 16 + -16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + -16 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + -16 Combine like terms: 0 + -16 = -16 4X + 2iX + -2ix + -4i2 + 4x + xX = -16 Add '2ix' to each side of the equation. 4X + 2iX + -2ix + -4i2 + 4x + 2ix + xX = -16 + 2ix Reorder the terms: 4X + 2iX + -2ix + 2ix + -4i2 + 4x + xX = -16 + 2ix Combine like terms: -2ix + 2ix = 0 4X + 2iX + 0 + -4i2 + 4x + xX = -16 + 2ix 4X + 2iX + -4i2 + 4x + xX = -16 + 2ix Add '4i2' to each side of the equation. 4X + 2iX + -4i2 + 4x + 4i2 + xX = -16 + 2ix + 4i2 Reorder the terms: 4X + 2iX + -4i2 + 4i2 + 4x + xX = -16 + 2ix + 4i2 Combine like terms: -4i2 + 4i2 = 0 4X + 2iX + 0 + 4x + xX = -16 + 2ix + 4i2 4X + 2iX + 4x + xX = -16 + 2ix + 4i2 Add '-4x' to each side of the equation. 4X + 2iX + 4x + -4x + xX = -16 + 2ix + 4i2 + -4x Combine like terms: 4x + -4x = 0 4X + 2iX + 0 + xX = -16 + 2ix + 4i2 + -4x 4X + 2iX + xX = -16 + 2ix + 4i2 + -4x Reorder the terms: 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = -16 + 2ix + 4i2 + -4x + 16 + -2ix + -4i2 + 4x Reorder the terms: 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = -16 + 16 + 2ix + -2ix + 4i2 + -4i2 + -4x + 4x Combine like terms: -16 + 16 = 0 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + 2ix + -2ix + 4i2 + -4i2 + -4x + 4x 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 2ix + -2ix + 4i2 + -4i2 + -4x + 4x Combine like terms: 2ix + -2ix = 0 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + 4i2 + -4i2 + -4x + 4x 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 4i2 + -4i2 + -4x + 4x Combine like terms: 4i2 + -4i2 = 0 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 + -4x + 4x 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = -4x + 4x Combine like terms: -4x + 4x = 0 16 + 4X + 2iX + -2ix + -4i2 + 4x + xX = 0 The solution to this equation could not be determined.
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