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