Is there a way to take Euler's formula "e^(i∅)" -which gives a circle; and change it into a logarithmic spiral?(adsbygoogle = window.adsbygoogle || []).push({});

Does a simple modification like " e^-(i∅/n) " make any sense mathematically?

If it actually does, my other question would be; supposing that such a logarithmic spiral is in fact just a head on view of a space curve with parameters like:

y=tsint

x=tcost

z=e^(-t/12)

how does one go about finding the arc length of such a curve? I've attempted to use the general arc length formula on this one, but continually end up with something like:

s = ∫ √e^-t/12 + t^2 + 1

which is, apparently, impossible to solve.

Is there a way to use the complex variable in a formula like Euler's formula to create a logarithmic spiral? And if so, how does one go about calculating the arc length of such a thing?

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# Can we change Euler's Formula?

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