Euler's Formula and Complex Logarithms relationship

[physicsdreams]

I've become rather curious, as of late, about the realm of complex logarthims; more specifially logarithms in the form log(z) where z is any negative number.
Excuse any ignorance on my part, as I'm only in Precalculus, but I was just curious to see how Euler's formula is related to complex logarithms.

If anyone can explain this in Laymen's terms (I know this is the Calculus section, but I didn't think this topic belonged in the general math section) keeping in mind that I have no Calculus experience, that would be great.
Any outside resources that break it down would also be helpful.

Sorry if I'm asking the impossible, i.e. Calc without Calc.

Thanks.

 

[mathman]

Complex numbers are usually represented in either of two ways. z= x + iy (rectangular), where x and y are real, or z = re^iθ (polar), where r is non-negative real and 0 ≤ θ < 2π.
If you use the polar form ln(z) = ln(r) + iθ. For negative reals θ = π.

Also note that the log is multivalued, since adding integer multiples of 2π doesn't change the value of z in polar form.