## 2bornot2b 3 years ago What is the difference between exp(z) and $$e^z$$. z is complex.

1. imranmeah91

I didn't know there was any

2. satellite73

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

3. asnaseer

no difference - they are synonyms

4. amistre64

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

5. amistre64

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

6. 2bornot2b

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

7. amistre64

is Log e = 1?

8. 2bornot2b

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

9. amistre64

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

10. 2bornot2b

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

11. 2bornot2b

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

12. satellite73

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

13. 2bornot2b

Yes, right, that is why I mentioned it

14. 2bornot2b

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

15. satellite73

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

16. 2bornot2b