  During my study of the iteration of functions of the form
$f(z)=z^{\alpha}+c$, where $z,c \in \mathbbC$, and $\alpha$ is a rational
non-integer larger than 2 (\cite{s1}), I encountered a fundamental difficulty
in the exponentiation of a complex number. This paper will explore this
difficulty and the problems encountered in trying to resolve it using a Riemann
surface which is the direct generalization of the polar form of the complex
plane. This paper will also answer two questions raised by Robert Corless in
his \emph{E.C.C.A.D.} presentation \cite{co}: "Can a Riemann surface variable
be coded? What will the operations be on it?" Unfortunately, the addition
operation will be incompatible with the Riemann surface structure.
