Does
$$\left|\lim\_{N \rightarrow \infty} f(N)\right|^2 = \lim\_{N \rightarrow \infty} |f(N)|^2, \tag{1}$$
where $f(N)$ is a function of $N$ and $N$ is a natural number?

Here is my try: $y(x)=|x|^2$ is a continuous function of $x$, so (1) is true. Am I right?