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 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 $z=re^{i \theta}$ so $z^a=r^a e^{i a \theta$ so if we change $\theta$ by $2 \pi$ we have the same value of z corresponding to more than one value of $z^a$ (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"?