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2bornot2b Group Title

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

  • 2 years ago
  • 2 years ago

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  1. imranmeah91 Group Title
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    I didn't know there was any

    • 2 years ago
  2. satellite73 Group Title
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    notation i think unless i am sadly mistaken they are the same

    • 2 years ago
  3. asnaseer Group Title
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    no difference - they are synonyms

    • 2 years ago
  4. amistre64 Group Title
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    since exponents can get pretty messy; the exp(...) notation is for clarity

    • 2 years ago
  5. amistre64 Group Title
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    the of exp(..) as a similar notation to log(...)

    • 2 years ago
  6. 2bornot2b Group Title
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    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

    • 2 years ago
  7. amistre64 Group Title
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    is Log e = 1?

    • 2 years ago
  8. 2bornot2b Group Title
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    \(Logz=e^{logr}+i\theta +2ni\pi\) where \(z=r(cos\theta+isin\theta)\)

    • 2 years ago
  9. amistre64 Group Title
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    http://math.furman.edu/~dcs/courses/math39/lectures/lecture-17.pdf this might be useful

    • 2 years ago
  10. 2bornot2b Group Title
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    So Log e is a multivalued function. It has an infinite number of values and 1 is one of the values it takes.

    • 2 years ago
  11. 2bornot2b Group Title
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    Can you all guide me somewhere, like a book or may be an user of OS, who can help on this

    • 2 years ago
  12. satellite73 Group Title
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    actually as i recall the notation Log is single values whereas log is multivalued, but i could be wrong

    • 2 years ago
  13. 2bornot2b Group Title
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    Yes, right, that is why I mentioned it

    • 2 years ago
  14. 2bornot2b Group Title
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    So as to avoid any confusion. @satellite73 you are right, but some books write it the other way round.

    • 2 years ago
  15. satellite73 Group Title
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    \[\log(z)=\ln(|z|)+i\theta\] for any \(\theta\) whereas \[Log(z)=\ln(|x|)+i\theta\] for \[-\pi\leq\theta\leq\pi\]

    • 2 years ago
  16. 2bornot2b Group Title
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    @Zarkon can you help please?

    • 2 years ago
  17. 2bornot2b Group Title
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    @amistre64 You have provided a great link. So I choose your answer as the best answer.

    • 2 years ago
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