How do you use the binomial series to expand #sqrt(1+x)#?
Use the generalization of the binomial formula to complex numbers.
There is a generalization of the binomial formula to the complex numbers.
The general binomial series formula seems to be
This is a power series so obviously, if we want to have chances that this doesn't diverge we need to set
I'm not going to demonstrate the formula is true, but it's not too hard, you just have to see that the complex function defined by