I have the quaternions $q = x_0 + ix_1 + jx_2 + kx_3$ where $x_i \in \mathbb{R}$ and $i,j,k$ satisfy the relations $$ i^2=j^2=k^2 = -1, \hspace{0.3cm} ij=-ji=k,\hspace{0.3cm} jk=-kj=i,\hspace{0.3cm} ki=-ik=j$$ I also have that $f(q) =q^2$ defines a smooth map from $\mathbb{R}^4 \cup \{\infty\} \cong S^4$ to itself.
I have to find the degree of f. Can someone help me ?