Euler's Formula and Complex Logarithms relationship

  • #1

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
mathman
Science Advisor
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Complex numbers are usually represented in either of two ways. z= x + iy (rectangular), where x and y are real, or z = re (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.
 

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