Let [tex]f(x+iy)=u(x,y)+iv(x,y)[/tex]. Suppose we know [tex]|f|^2=u^2+v^2[/tex] is a constant function. Then we are allowed to say that [tex](u^2+v^2)_x=(u^2+v^2)_y=0[/tex]. But are we allowed to differentiate u by x and v by y? IE, are we allowed to make the following statement:(adsbygoogle = window.adsbygoogle || []).push({});

[tex](u^2)_x+(v^2)_y=0[/tex]

I'm guessing 'no', but I'm not too sure why. Intuitively, I would guess that you could change u and v in such a way that those changes balance each other out? (Very unclear way to say it...)

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# Homework Help: Technical question in multi-variable differentiation

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