Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose $f(z) = z^2$

This function has the component functions $u(x,y) = x^2 - y^2$, $v(x,y) = 2xy$

And it says in a book I'm reading that $v$ is a harmonic conjugate of $u$. But v is not harmonic as

$v_{xx} = 2$ and $v_{yy} = 2$

So $v_{xx} + v_{yy} = 4 \not= 0$

So how can it say that v is a harmonic conjugate of u? I presume I'm missing something as I don't think the book is wrong.

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

$$\partial_x 2xy = 2y$$$$\partial_x 2y = 0$$Similarly, $\partial_{yy} 2xy = 0$, and sure enough 0 + 0 = 0!

share|improve this answer
    
lol, note to self, write stuff out on paper fully. –  Jim_CS Apr 30 '12 at 11:25
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.