Cauchy-Riemann Question

  • Thread starter tylerc1991
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  • #1
tylerc1991
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Homework Statement


Show that f'(z) DNE

f(z) = e^x * e^-iy

Homework Equations



so I have to show that u_x =/= v_y or v_x =/= -u_y

The Attempt at a Solution



my question is this: what is u(x,y) and v(x,y)? is it e^x and e^-iy respectively? Thank you for your help!
 

Answers and Replies

  • #2
Dick
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You have to write f=u+iv where u and v are real functions. e^(-iy) isn't a real function. And there's a '*' between them, not a '+'.
 
  • #3
tylerc1991
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That is the basis of my question, how would I write that function in f(z) = u + iv? e^(x-iy)?
 
  • #4
Dick
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That is the basis of my question, how would I write that function in f(z) = u + iv? e^(x-iy)?

Use deMoivre. e^(it)=cos(t)+i*sin(t).
 
  • #5
tylerc1991
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ahh I see, thank you!!!
 

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