I know they are similar in the sense of
but is there any more of a connection between logarithms and angles?
My teacher says there is.
I think the similarity may be like this
1- like we define log (a) we can define sin (a) where sin is a function like log
2- As you can find the value of log (a), similarly you can find the value of sin (a).
3- like you can find the anti logarithm similarly you can find inverse
e.g if log (a)=b then antilog(b) = a and if sin (a) = b then sin^-1 (b) = a
i hope this will help you.........
exp(I*theta) = e^(I*theta) = cos(theta) + I*sin(theta)
where I^2 = -1.
Now, the inverse of the exp() function is the "natural logarithm" function, ln(). So what happens is that:
exp(I*alpha) * exp(I*beta) = exp(I*[alpha + beta])
ln[exp(I*alpha) * exp(I*beta)] = I*(alpha + beta)
arg[exp(I*alpha) * exp(I*beta)] = alpha + beta
so you can see a similarity.
The things Dan has said on this topic are very much correct and a bit advanced as compared to my answer. I did not say all those as I thought he/she may not be able to catch.
By the way it is really nice the things to get solved....Keep it up Dan!!!!
Good luck and be in touch Dan in my e-mail may be email@example.com