An archived instance of discourse for discussion in undergraduate Complex Variables.

Continuity of a function

lszabo

We learned about continuity during last class and I found an interesting problem regarding it. The question asks one to find all points of continuity of the function $h(z)$ where
\[ h(z) = \begin{cases}
z & |z| \leq 1 \\
|z| ^2 & |z| > 1\\
\end{cases}
\]