Lindemann–Weierstrass theorem

In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α₁, ..., α_n are algebraic numberswhich are linearly independent over the rational numbers Q, then e^α₁, ..., e^α_n are algebraically independent over Q; in other words the extension field Q(e^α₁, ..., e^α_n) has transcendence degree n over Q.