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Let z be a non-real complex number for which the expression (1 + z + z²)/(1 - z + z²) is a real number. What is the value of |z|?

1. 1
2. 2
3. 1/2
4. sqrt(2)

Correct answer: 1

Solution

Forcing the ratio to be real (equal to its conjugate) and using z != conj(z) for a non-real z leads to |z|² = 1, so |z| = 1.

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