I'm working on Example $4$, page $262$, of Harris Hancock's book *Lectures on the Theory of Elliptic Functions* which reads:

Prove that $\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\operatorname{sn}(u,k)^2} = 1$.

I can only get this result if $\operatorname{sn}(u,k) = \operatorname{sn}(u,k')$, where $k'$ is the complimentary modulus of $k$. But that does not make sense.