- #1
kcuf
- 6
- 0
I understand the basic definitions and ideas behind choosing branches of multivalued functions, but I still have some uncertainty when dealing with multivalued functions. As an example, if I'm in the the principal branch, when can I say that $(z-1)^\frac 1 2(z+1)^\frac 1 2= (z^2-1)^\frac 1 2$; or, what happens when I differentiate $\sqrt z$ in the principal branch, the resulting derivative is $z^{-\frac 1 2}$, am I free to choose whatever branch I want for this derivative, or does it have to correspond to that of the original function.
If anyone could help me clarify this, I would greatly appreciate it.
Thanks
If anyone could help me clarify this, I would greatly appreciate it.
Thanks