I don't know if technically challenging can be interpreted as finding the right trick (which can be quite difficult) to prove it. If so, then the Hahn-Banach theorem should be included. While the real version has a natural proof, the complex version involves a trick that is not obvious. According to what I remember (probably apocryphal), it took Banach two years to obtain the complex version after he had proved the real version.

And of course, H-B is used all the time in functional analysis.