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\\

f(z)=\left\{\begin{array} \frac{(\bar{z})^2}/ {z} \quad z\neq0 \\

0 \quad z=0

\end{array}

\right.\)

**Show that f is differentiable at z=0, but the Cauchy Riemann Equations hold at z=0.**

Well i have tried to start the first part but i am stuck, could you please help me out.

**WORKING:**f is diff at z=0

if \(\displaystyle \lim_{z \to 0} \frac{f(z)-f(0)}{z-0}\; exists\\

\lim_{z\to0}\frac{ \frac{(\bar{z})^2}{z}-0}{z-0}=

\lim_{z\to0}\frac{(\bar{z})^2}{z^2}

\)

Now we get indeterminate form in the limit but how can we differentiate \(\displaystyle \bar{z}\)