(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that

[tex] ln(z^\alpha) = \alpha ln(z) [/tex]

where 'z' and 'alpha' are complex.

2. Relevant equations

[tex]ln \alpha = ln r + i(\theta + 2*n*\pi) [/tex]

3. The attempt at a solution

For the left hand side I have [tex] ln (z^\alpha) = ln [(r_{1}e^(i\theta_{1}))^(r_{2}e^(i\theta_{2}))][/tex]

and for the right [tex] \alpha ln(z) = \alpha [ln r + i(\theta + 2 n \pi)] [/tex]

I have played with it for a bit but seem to be going in circles...

Any tips/hints would be greatly appreciated! Thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The complex logarithm

**Physics Forums | Science Articles, Homework Help, Discussion**