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I need to determine where the following function is differentiable and holomorphic in $\mathbb C$:

$$f(z)=(z-3)^i$$

I have the derivative as $df/dz= i(z-3)^{-1+i}$. The answer in my book says f is differentiable and holomorphic on $\mathbb C$ where $y\neq0$ and $x>3$. I don't see where this comes from. wolframalpha plotted the derivative and I can see that the imaginary part has a vertical asymptote at 0, but I can't see why f is not differentiable or holomorphic for $x\leq3$. How can I find the answer by looking at the function and its derivative?

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