A function is differentiable if and only if there exists a linear function such that .
Edit: for the function defined by , define where . Then:
Hello mathematicians,
I am asked to study the differentiability of lzl^{2} (complex analysis) and don't know how to do it :_(
I've read that it is only differentiable at 0, but how to reach that conclusion I ignore.
The two ways that I know for checking if a function is differentiable are
(1) By checking if the limit definition of derivative exists
But I don't know how to work with the squared modulus of numbers adding (numerator of the limit), and I don't think that's the way I'm supposed to do it...
(2) Checking where C-R equations hold. However, modulus(z)^2 doesn't have imaginary part, so I don't have u and v.
How can I study the differentiability of this function then?? I don't know to do this for f(z)=Re(z) either.
Thank you!