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## Homework Statement

Give the location and orders of the branch points at, and classify the singularities [itex]f(z) =\frac{1}{z^{1/2}}[/itex]

**Mod note**: Fixed LaTeX in exponent above and below.

To OP: To write a fractional exponent such as ##z^{1/2}## use braces around the exponent, like this: ##z^{1/2}##. It works the same using the tex and itex tags.

## Homework Equations

## The Attempt at a Solution

My initial thought is there is a pole at z=0 of order 1/2? But I don't think you can have fractional order poles? So maybe I need to get the Laurent expansion for [itex]f(z) =\frac{1}{z^{1/2}}[/itex] about z=0? but I'm not too sure how to approach this?

Since we require z to 'go around' the complex plane twice to return to our original value is the branch cut of order 1?

I would assume that regardless of the order the branch cut extends along the real axis of the complex plane from 0 to infinity.

Many thanks :)

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