Find all points where the function has a derivative. At which of these points the function is analytical.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

f(z) = \left\{

\begin{array}{ll}

{z^2}sin(\frac{1}{|z^2|}) & z \neq 0 \\

0 & z = 0}

\end{array}

\right.

[/tex]

I have tried deriving directly using the limit and also tried using Cauchy-Riemann, both tries led to complicated formulas.

For example Cauchy-Riemann approach:

[tex]

f(a+ib) = \underbrace{ (a^2-b^2)sin(1/\sqrt{a^2+b^2})}_{u} +

i\underbrace{{2ab}\cdot{sin(1/\sqrt{a^2+b^2})}}_{v}

[/tex]

Now I need to calculate dv/da ,du/da ,dv/db,du/db, but this seems like a headache.

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# Homework Help: Complex Deriviative

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