% Homework for Physical Mathematics I
% Ewan Stewart
% KAIST
% 2011/10/11

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\begin{document}

\begin{homework}
[Optional extra question.]

\question{integration}

Let $f(z,z^*)$ be a complex function and $\vect{f}$ be the vector field on the complex plane with Cartesian components $(\Re f,\Im f)$.
Show that
\begin{equation} \label{stokes}
\int_{\partial A} f \d{z^*} = \int_A \left( \vect\nabla \wedge \vect{f} - i \vect\nabla \cdot \vect{f} \right) \d{A}
\end{equation}
where $\partial A$ is the boundary of the area $A$ in the complex plane.
Interpret
\begin{equation} \label{charge}
f = \frac{1}{2\pi z^*}
\end{equation}
in terms of two dimensional electromagnetism.

\end{homework}

\end{document}

