- #1
jpb1980
- 5
- 0
Find a (complex) polynomial function f of x and y that is differentiable at the origin, with
df/dz = 1 at the point z=0, and differentiable at all points on the unit circle x^2 + y^2=1, but is not differentiable at any other point in the complex plane. (Bruce Palka, Page 101)
I think we use the Cauchy Riemann relations. I am having a hard time with this one.
I have tried (1+x^2 +y^2) + (1 + x^4 + 2 x^2 y^2 + y^4)*i but that did not work.
df/dz = 1 at the point z=0, and differentiable at all points on the unit circle x^2 + y^2=1, but is not differentiable at any other point in the complex plane. (Bruce Palka, Page 101)
I think we use the Cauchy Riemann relations. I am having a hard time with this one.
I have tried (1+x^2 +y^2) + (1 + x^4 + 2 x^2 y^2 + y^4)*i but that did not work.