Monday, November 04, 2013
\(Re(z), \, \bar z\) & \(\lvert z \rvert^2 \)
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:
| \[ \begin{aligned} f(z) &= \text{Re }(z) \\ f(z) &= \bar z \\ f(z) &= \lvert z \rvert^2 \end{aligned} \] |
