How do you show that a complex function is analytical?

  • #1

Main Question or Discussion Point

Like if I wanted to show how sin z, cos z, or e^z are analytical, what is the general process I have to do? Can I use the cauchy - riemann relations somehow?

(where z = x + iy is complex)
 

Answers and Replies

  • #2
LCKurtz
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Yes. For example, ez = ex+iy = exeiy =ex(cos(y) + i sin(y)) so

u = excos(y) and v = exsin(y)

and you can Cauchy-Riemann away.
 
  • #3
Thanks! :)
 

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