The limit of $|z|^2/z$ in the complex plane What is the limit of $|z|^2\over z$ in the complex plane at $z_0=0$?
This is how I do it: ${|z|^2\over z}={{x^2+y^2}\over {x+iy}} $, then along the real axis, and the imaginary axis, the limit approaches different value, namely $y/i$ and $x$, so the limit DNE. Is that correct?

Let $f(z)=|z|^2/z$ then
$$\lim_{z\to0}|f(z)|=|z|=0$$
so
$$\lim_{z\to0}f(z)=0$$
