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I didn't know there was any

notation i think
unless i am sadly mistaken they are the same

no difference - they are synonyms

since exponents can get pretty messy; the exp(...) notation is for clarity

the of exp(..) as a similar notation to log(...)

is Log e = 1?

\(Logz=e^{logr}+i\theta +2ni\pi\) where \(z=r(cos\theta+isin\theta)\)

http://math.furman.edu/~dcs/courses/math39/lectures/lecture-17.pdf
this might be useful

Can you all guide me somewhere, like a book or may be an user of OS, who can help on this

Yes, right, that is why I mentioned it

@amistre64 You have provided a great link. So I choose your answer as the best answer.