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## Homework Statement

This problem seems fine but has me stumped for some reason...

For the variables

u=x

^{2}−y

^{2}

v= x y

Under the condition u>0

We're simply asked to determine x(u,v) and y(u,v) so that we can eventually use them to solve a multiple integral by substitution.

## Homework Equations

## The Attempt at a Solution

I've tried a number of different methods - for example, trigonometric and hyperbolic substitutions for x and y, various linear and quadratic combinations of u and v, etc. - and for some reason I can't find a simple way of expressing x and y in terms of u and v. I noticed that if you let z=x+yi then R(z2)=u and I(z2)=2v, but I'm not sure how this helps. I know there's something really simple I must be overlooking, but any help would be greatly appreciated.

I can actually solve the integral they gave us - which is pretty easy - just by finding the jacobian d(u,v)/d(x,y) and using the fact that this is the inverse of the Jacobian d(x,y)/d(u,v) without ever explicitly determining the function in terms of u and v - doing it this way, nice factors in the integrand cancel out, which I'm guessing was the point of the question - but I still can't find x (u,v) and y (u,v).