Prove that $$\lim_{z \to 0} \dfrac{\bar{z}}{z}\;\text{ does not exist.}$$
Not sure how to prove this. Any suggestions would be great!
Prove that $$\lim_{z \to 0} \dfrac{\bar{z}}{z}\;\text{ does not exist.}$$
Not sure how to prove this. Any suggestions would be great!
Consider $z = r e^{i \theta}$, then
$$ \frac{\overline{z}}{z} = e^{-2 i \theta} $$
and this depends on the direction $\theta$.
Just look at the result you get when you let $z = x+0i$, and let $x$ tend to 0.
Then do the same with $z = 0 + iy$ and let $y$ tend to zero.
For the limit you want, the answers to the above two would have to be the same, but as you find ...