A complex function $f$ is analytic if $f$ is differentiable at each point $z \in U$ where $U$ is an open set in $\mathbb{C}$. A function which is analytic in all of $\mathbb{C}$ is called an entire function.

Consider the complex functions:

$$\begin{aligned} f(z) &= \text{Re }(z) \\ f(z) &= \bar z \\ f(z) &= \lvert z \rvert^2 \end{aligned}$$

Can you see why they are not analytic ?

# posted by rot13(Unafba Pune) @ 7:57 PM