2bornot2b
  • 2bornot2b
What is the difference between exp(z) and \(e^z\). z is complex.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I didn't know there was any
anonymous
  • anonymous
notation i think unless i am sadly mistaken they are the same
asnaseer
  • asnaseer
no difference - they are synonyms

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amistre64
  • amistre64
since exponents can get pretty messy; the exp(...) notation is for clarity
amistre64
  • amistre64
the of exp(..) as a similar notation to log(...)
2bornot2b
  • 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
amistre64
  • amistre64
is Log e = 1?
2bornot2b
  • 2bornot2b
\(Logz=e^{logr}+i\theta +2ni\pi\) where \(z=r(cos\theta+isin\theta)\)
amistre64
  • amistre64
http://math.furman.edu/~dcs/courses/math39/lectures/lecture-17.pdf this might be useful
2bornot2b
  • 2bornot2b
So Log e is a multivalued function. It has an infinite number of values and 1 is one of the values it takes.
2bornot2b
  • 2bornot2b
Can you all guide me somewhere, like a book or may be an user of OS, who can help on this
anonymous
  • anonymous
actually as i recall the notation Log is single values whereas log is multivalued, but i could be wrong
2bornot2b
  • 2bornot2b
Yes, right, that is why I mentioned it
2bornot2b
  • 2bornot2b
So as to avoid any confusion. @satellite73 you are right, but some books write it the other way round.
anonymous
  • anonymous
\[\log(z)=\ln(|z|)+i\theta\] for any \(\theta\) whereas \[Log(z)=\ln(|x|)+i\theta\] for \[-\pi\leq\theta\leq\pi\]
2bornot2b
  • 2bornot2b
@Zarkon can you help please?
2bornot2b
  • 2bornot2b
@amistre64 You have provided a great link. So I choose your answer as the best answer.

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