- #1
Fabio010
- 84
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The question is to check where the following complex function is differentiable.
w=z \left| z\right|
w=\sqrt{x^2+y^2} (x+i y)
u = x\sqrt{x^2+y^2}
v = y\sqrt{x^2+y^2}
Using the Cauchy Riemann equations
\frac{\partial }{\partial x}u=\frac{\partial }{\partial y}v
\frac{\partial }{\partial y}u=-\frac{\partial }{\partial x}v
my results:
\frac{x^2}{\sqrt{x^2+y^2}}=\frac{y^2}{\sqrt{x^2+y^2}}
\frac{x y}{\sqrt{x^2+y^2}}=0
solutions says that it's differentiable at (0,0). But doesn't it blow at (0,0)?
w=z \left| z\right|
w=\sqrt{x^2+y^2} (x+i y)
u = x\sqrt{x^2+y^2}
v = y\sqrt{x^2+y^2}
Using the Cauchy Riemann equations
\frac{\partial }{\partial x}u=\frac{\partial }{\partial y}v
\frac{\partial }{\partial y}u=-\frac{\partial }{\partial x}v
my results:
\frac{x^2}{\sqrt{x^2+y^2}}=\frac{y^2}{\sqrt{x^2+y^2}}
\frac{x y}{\sqrt{x^2+y^2}}=0
solutions says that it's differentiable at (0,0). But doesn't it blow at (0,0)?
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