I was trying to find solution to $\arg(z+w)$, where $z$ and $w$ are two complex numbers in terms of $\arg(z)$ and $\arg(w)$.
Making a parallelogram out of vector addition of the $2$ complex numbers in Argand plane leads to $$\arg(z+w)=\frac{\arg(z)+\arg(w)}{2}$$
Am I correct or there are some cases to be accounted for?
(consider only principal arguments)
Best Answer
In order to compute $\arg(z+w)$ you will need to know not only $\arg z$ and $\arg w$, but also $|z|$ and $|w|$. Then it is a trigonometry problem.