I've read about complex logarithms and maybe it's just my reading skill, but it all seems to be way too complicated. Anyways, after doing some thinking of my own I've come up with a few formulas, one of which is ln(-a) = ln(a) + πi; however, my reasoning behind such formulas seems way too basic, so I'm doubting myself. Could someone please check my work and let me know if what I'm doing is ok?(adsbygoogle = window.adsbygoogle || []).push({});

Here's the derivation:

ln(-a) = ln(-a)

ln(-a) = ln(-1a)

ln(-a) = ln(-1) + ln(a) -- Properties of Logs

ln(-a) = πi + ln(a) -- Euler's Identity

Euler's identity states e^(iπ) = -1; therefore, ln(-1) = iπ.

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# Is this formula justified?

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