Dual and degree of the isogeny a+b[i].

Question

Let $[i]$ be the endomorphism such that $[i](x,y) = (-x,iy)$ with $[i]^2+[1]=[0]$. I am trying to prove that the degree of the endomorphism $[a]+[b]\circ[i]$ is equal to $a^2+b^2$. After multiplication in $End(E)$ by $[a]+[-b]\circ[i]$ I get $[a]^2+[b]^2$. I now have two endomorphisms whose composition is $[a^2+b^2]$. Is this enough for me to conclude that the dual of $[a]+[b]\circ[i]$ is equal to $[a]+[-b]\circ[i]$ and that the degree is equal to $a^2+b^2$? Theorems about the existence of the dual seem to start with the assumption that you know the degree already.