2
votes
0answers
61 views

Interpretation of a line integral in complex analysis

$\newcommand{\C}{\mathbb{C}}$ Suppose $f\colon \Omega\subset \C\to\C$ is a holomorphic function and $\gamma:[0,1]\to\Omega$ is a continuous path. If $\Omega=\C\setminus\{0\}$, $\gamma(t):= e^{2\pi i ...
0
votes
0answers
156 views

product $abababab…$ in clifford algebra

Let $a,b$ are vectors in vector space $V \leq \mathcal{Cl}_n(V)$. I would like to know if product $ababab...ab=(ab)^r$ can be written in form $\sum_{\alpha \in A} F_\alpha(a) G_\alpha(b)$. For some ...
4
votes
3answers
92 views

When does the next complex split occur?

So I was thinking about complex numbers and how they came about and someting interesting occured to me: the formation of complex numbers occurs because there exists a function (namely $f(x)=x^2$) ...