Does Z gate swap complex amplitudes of $|0\rangle$ and $|1\rangle$?

Question

I am reading Quantum Computing 1st Edition By Parag Lala, this book says

It seemed that the Z gate swapped the complex amplitudes $\alpha$ and $\beta$.

Can Z gate implement that, or are there any errata? Because

$$ \begin{pmatrix} \alpha \\ -\beta \end{pmatrix} = \alpha\begin{pmatrix} 1 \\ 0 \end{pmatrix} - \beta\begin{pmatrix} 0 \\ 1 \end{pmatrix} \neq \alpha\begin{pmatrix} 0 \\ 1 \end{pmatrix} + \beta\begin{pmatrix} 1 \\ 0 \end{pmatrix} = \alpha|1\rangle + \beta|0\rangle $$

And, is it true that Z Gate merely add $\pi$ to the relative phase $\phi$ of a superposition $|q\rangle$?

$$ |q\rangle = \alpha|0\rangle + e^{i\phi}\beta|1\rangle $$ $$ Z|q\rangle = \alpha|0\rangle + e^{i(\phi+\pi)}\beta|1\rangle $$

Answer 1

This is wrong for sure.

And according to the book reviews on Amazon, this book is "unreliable", "riddled with errors", and "someone studying for the first time will get confused"