Apparently there is no need for a branch cut for this function, but I am not sure why - I heard it has something to do with cos being an even function. Any clarification would be appreciated.
I'm sure you've done an exercise like writing down all of the values of a multivalued function like sqrt(z) in terms of ordinary functions. (e.g. in terms of the principal branch Sqrt(z))
I'm sure you've done an exercise like writing down all of the values of a multivalued function like sqrt(z) in terms of ordinary functions. (e.g. in terms of the principal branch Sqrt(z))
That seems like an obvious place to start to me.
You mean write z as r*exp(i(t+2*k*pi)), so sqrt(z) = (r^1/2)*exp(it/2) or (r^1/2)*exp(i(t/2+pi)? = -(r^1/2)*exp(it/2) ?
