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analytic_function [2014/03/21 11:11] 127.0.0.1 external edit |
analytic_function [2014/11/30 18:38] nikolaj |
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| - | A complex function $f(z)$ consists of two real functions, so it's fence height is just given by the sum of the fence heigh of \mathrm{Re}\,f(z)$ and $i\,\mathrm{Im}\,f(z)$. Let's consider the function $f(z):=z=r\,\cos\theta+i\,r\,\sin\theta$. We have | + | A complex function $f(z)$ consists of two real functions, so it's fence height is just given by the sum of the fence heigh of $\mathrm{Re}\,f(z)$ and $i\,\mathrm{Im}\,f(z)$. Let's consider the function $f(z):=z=r\,\cos\theta+i\,r\,\sin\theta$. We have |
| $z^n=r^n\,\mathrm{e}^{i\,n\,\theta}=r\,\cos(n\,\theta)+i\,r\,\sin(n\,\theta)$ | $z^n=r^n\,\mathrm{e}^{i\,n\,\theta}=r\,\cos(n\,\theta)+i\,r\,\sin(n\,\theta)$ | ||
