The question says:
Let $\;z\;$ and $\;w\;$ be two non-zero complex numbers such that $|z|=|w|$ and $amp(z)+amp(w)=\pi,\;$ then find a relation between $\;z\;$ and $\;w.$
In the solution they turn $ amp(z)+amp(w)$ into $amp(Z)-amp(\overline w)\;$ and equate it to $\pi$. What was the need to do so ? I think I may be missing some concept.
The final answer is $\;z+ \overline w=0.$