I may be missreading your question.
But the usual way of doing this is: .
Is that close to what ou mean?
I'm not sure how to go about solving this little question...
By expressing z = i*r*e^(i*theta) in terms of 'z'*e^(i*theta) ('z' is the modulus of z), find the natural logarithm of z.
I have thought of a couple of different approaches but the answers end up looking quite inelegant, so I think they may be wrong... and there's no answer in the back of the book...
Thank you very much in advance!