## Relationship between integral bases and discriminants

Suppose $[K:\mathbb{Q}] = n$, and that there are $r$ real embeddings and $s$ pairs of complex embeddings of $K$ into $\mathbb{C}$, where $r+2s = n$. Show that if $w=\{w_1,...,w_n\}$ is an integral basis for $\mathcal{O}_K$ then the sign of $\triangle(w)^2$ is $(-1)^s$.