If $a$ and $b$ are two complex numbers, and $a \neq 0$, then how to show that the condition required for $|a+b| = |a| + |b|$ is $b/a$ is real and non-negative.
I did the following and I got stuck
$ \hspace{12 mm}|a+b|^2 = (|a| + |b|)^2 \\ \implies (a+b)(\bar a + \bar b) = |a|^2 + 2|a||b| + |b|^2 \\ \implies \bar a b + a \bar b = 2|a||b|$