(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!

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# The complex logarithm

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