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How do you show that a complex function is analytical?

  1. Mar 17, 2010 #1
    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)
     
  2. jcsd
  3. Mar 17, 2010 #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.
     
  4. Mar 18, 2010 #3
    Thanks! :)
     
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