Thread: Holomorphic
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latentcorpse
latentcorpse is offline
#3
Mar19-09, 04:22 PM
P: 1,431
ok. is this possible using the Cauchy Riemann equations though?

also can you talk me throught the branch cut here:

we have [latex]z=re^{i \theta}[/latex]
so [latex]z^a=r^a e^{i a \theta[/latex]

so if we change [latex]\theta[/latex] by [latex]2 \pi[/latex] we have the same value of z corresponding to more than one value of [latex]z^a[/latex] (i.e. a multifunction). This means there are different branches corresponding to the different values the function can take for the same z.
what do you mean by "take a branch cut along the negative real axis"?