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Complex power raised over real number.

  • Thread starter PrashntS
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  • #1
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1. I actually dont know if such kind of operation is even allowed.

A friend of mine raised this question, that can we raise a complex power over a real number. I solved it this way. Is this correct?

http://i45.tinypic.com/254vwux.jpg

Homework Statement





Homework Equations





The Attempt at a Solution

 
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Answers and Replies

  • #2
SammyS
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Yes, that's fine.
 
  • #3
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Yes, you did it correctly. I am not quite sure approximating the transcandental functions with decimals, but I suppose that's fine.
 
  • #4
Ray Vickson
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1. I actually dont know if such kind of operation is even allowed.

A friend of mine raised this question, that can we raise a complex power over a real number. I solved it this way. Is this correct?

http://i45.tinypic.com/254vwux.jpg

Homework Statement





Homework Equations





The Attempt at a Solution

Your method is OK, but if you plan to use the results in further numerical computations, you should keep more digits of accuracy; nowadays, in this computer age, there is no barrier to retaining more digits. For example, it might be better (depending on future uses) to write
[tex]3^{5i} = e^{i 5 \ln 3 } = \cos(5 \ln 3) + i \sin(5 \ln 3) \doteq
0.7037573 - 0.7104404 i\, . [/tex]

RGV
 
  • #5
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Your method is OK, but if you plan to use the results in further numerical computations, you should keep more digits of accuracy; nowadays, in this computer age, there is no barrier to retaining more digits. For example, it might be better (depending on future uses) to write
[tex]3^{5i} = e^{i 5 \ln 3 } = \cos(5 \ln 3) + i \sin(5 \ln 3) \doteq
0.7037573 - 0.7104404 i\, . [/tex]

RGV
Yeah this is obviously much better, I was just looking whether it is even possible or not as none of the books I use has such question.
Would be awesome if you could suggest some good book for complex number (pre collage).
 
  • #6
Bacle2
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Are you also taking into account that there are infinitely-many solutions depending

on your choice of branch/argument?
 
  • #7
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Are you also taking into account that there are infinitely-many solutions depending

on your choice of branch/argument?
well thats obvious, isnt it? trigo fn is periodic, i just stayed in principle branch
 

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