Hi! I have this function:

And I want it harmonic conjugate f(z) where:

so I use cauchy-riemann equations:

So:

Why have i two diferents values for ?

Thanks!

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- March 19th 2010, 10:11 AMBop[SOLVED] Harmonic conjugate
Hi! I have this function:

And I want it harmonic conjugate f(z) where:

so I use cauchy-riemann equations:

So:

Why have i two diferents values for ?

Thanks! - March 19th 2010, 02:09 PMRandom Variable

so

then

and - March 20th 2010, 07:05 PMscorpion007
Because when you partially integrate with respect to you forgot to consider an arbitrary function of that was lost (since any function of differentiated w.r.t. is 0) and vice versa.

Another way of solving your problem:

(integrate w.r.t. y)

(integrate w.r.t. x)

Therefore, by inspection, must be , and .

So