Question: is there a misprint?

  • Thread starter Thread starter saraaaahhhhhh
  • Start date Start date
  • Tags Tags
    misprint
saraaaahhhhhh
Messages
21
Reaction score
0
This isn't a homework question; I'm sorry if I'm mis-posting, but I thought someone here could help.

See this link:
http://books.google.com/books?id=1Q...=intro+complex+analysis&lr=&as_brr=3#PPA56,M1

On page 56, does this book have a misprint in the definition of a differentiable complex function? On 5.1? Shouldn't the bottom of the quotient be 'h' instead of 'z'? I'm probably misreading or something. But I'm confused at why h is at the bottom of the quotient further down the page.

I don't know, maybe I'm being silly and there's something right there that I'm missing? Please help me out, thanks!
 
Physics news on Phys.org
Yes this is a misprint.

It looks corrected when they use it towards the bottom of the page.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top