What is the difference between exp(z) and $e^z$. z is complex.

Question

anonymous · Answer

I didn't know there was any

anonymous · Answer

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

asnaseer · Answer

no difference - they are synonyms

amistre64 · Answer

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

amistre64 · Answer

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

2bornot2b · Answer

I have a book which defines exp(z) as $e^x(cos y +isiny) $ where z=x+iy
and it defines $e^z~as~exp(z~Log~e)$ where Log is used to denote the multivalued Logarithmic function

amistre64 · Answer

is Log e = 1?

2bornot2b · Answer

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

amistre64 · Answer

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

2bornot2b · Answer

So Log e is a multivalued function. It has an infinite number of values and 1 is one of the values it takes.

2bornot2b · Answer

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

anonymous · Answer

actually as i recall the notation Log is single values whereas log is multivalued, but i could be wrong

2bornot2b · Answer

Yes, right, that is why I mentioned it

2bornot2b · Answer

So as to avoid any confusion. @satellite73 you are right, but some books write it the other way round.

anonymous · Answer

$$\log(z)=\ln(|z|)+i\theta$$ for any $\theta$ whereas $$Log(z)=\ln(|x|)+i\theta$$ for 
$$-\pi\leq\theta\leq\pi$$

2bornot2b · Answer

@Zarkon can you help please?

2bornot2b · Answer

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