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2bornot2b

  • 2 years ago

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

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  1. imranmeah91
    • 2 years ago
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    I didn't know there was any

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

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

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

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

  6. 2bornot2b
    • 2 years ago
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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

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

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

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

  10. 2bornot2b
    • 2 years ago
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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.

  11. 2bornot2b
    • 2 years ago
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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

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

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

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

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

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

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

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