The limit of $z\cdot\overline{z}$ as $z\to i$ How can I compute this limit:
$$\lim_{z\rightarrow i} (z\cdot \overline{z})$$
(where $\overline{z}$ is the conjugate of $z$)?

Hint: Is $z'$ the conjugate of $z$ and the lower dot a multiplication?  If so, what is the problem?  You might try expressing $z=a+bi$, with $a,b$ real and trying a real limit.
