Proving Non-Existence of f'(z) for f(z) = e^x * e^-iy | Cauchy-Riemann Question

[tylerc1991]

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!

 

[Dick]

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 '+'.

 

[tylerc1991]

That is the basis of my question, how would I write that function in f(z) = u + iv? e^(x-iy)?

 

[Dick]

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).

 

[tylerc1991]

ahh I see, thank you!