Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 1 down vote favorite

For what values of $p$ is the following valid? $$\log(z^p) = p\log(z)$$ where $$\log(z) = \ln(|z|) + i[\arg(z)+2\pi n]$$ where $n$ is an integer.

I heard the expression above should not be valid for all p so I computed $\log((1+i)^n)$ and $\frac1n \log(1+i)$ for $n = \frac12$ and $2$, but got the same answer so I know I've done something incorrectly.

share|improve this question
1  
Your expression for $\log(z)$ is not a function. You must choose a particular value for $n$. Then you can see where the problem lies. – ncmathsadist Feb 7 at 2:30
As already noted, it depends on what you mean by ''log''. Is it a particular branch (which one?) or a multi-valued expression? – mrf Feb 7 at 9:39

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.