- #1
DieCommie
- 157
- 0
Homework Statement
Show that
[tex] ln(z^\alpha) = \alpha ln(z) [/tex]
where 'z' and 'alpha' are complex.
Homework Equations
[tex]ln \alpha = ln r + i(\theta + 2*n*\pi) [/tex]
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!