The nth cyclotomic polynomial Φ‎_n(z) is the monic polynomial whose roots are the primitive n-th roots of unity. Φ‎₄(z) = z² + 1 as i and –i are the primitive fourth roots of unity.

When n is prime

Φ‎_n(z) = zⁿ⁻¹ + zⁿ⁻² + … + z + 1