arguments: the magnitude of e^(2 - 3i)

[lastlydreaming]

magnitude of e^(2 - 3i):

So with respect ot all of its arguments, does it become the following?

e^2 [(cos 3 + 2(pi)n) + i sin(3 + 2(pi)n)] where n = 0, +/- , +/- 2.... ?

Thanks.

 

[pka]

It seems to me as if you are missing the point.
For all z, \(\displaystyle \L e^{z + n\pi i} = e^z.\)

Thus \(\displaystyle \L \left| {e^{2 + ( - 3 + n\pi )i} } \right| = e^2\), period! For all n.