why is this function not complex-differentiable? [duplicate]

complex-analysis

Solution 1:

Consider $f(r e^{i \pi/4})$ for $r \to 0$ and conclude that $f$ is not even continuous at $z=0$.

Related

Help understanding a proof for "if a prime number $p$ divides $ab$ for $a,b \in \mathbb{N}$, then $p$ divides $a$ or $p$ divides $b$"
Solution to a non-convex problem — LP with unit norm constraint
Possible bug LaplaceTransform in Mathematica
Solving $D=\begin{vmatrix}a&\omega b&\omega^2c\\\omega^2b&c&\omega a\\\omega c&\omega^2a&b\end{vmatrix}$
Definition $f(x)$ diverges to negative infinity for $x \to a$
2nd order Taylor expansion of 2nd symmetric derivative
What is the maximum amount of "shore" tiles in a rectangular grid that has only "water" and "land" tiles?
Direct sum in physics
Does consistency of Peano arithmetic follow from arithmetical completeness of modal logic GL?
Showing that $x+x^2$ belongs to an ideal in $\mathbb{Z}_2[x]$
The elements of the centralizer of $A$ commute with all elements of $A\subseteq G$ and using this to prove that $C_G(A)$ includes inverses.
Power series of $1/(1-x-x^2)$