If z_1 and z_2 are two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then z_1-…

Question

If $z_1$ and $z_2$ are two non-zero complex numbers such that $|z_1+z_2|=|z_1|+|z_2|$, then $\arg z_1-\arg z_2$ is equal to

Accepted Answer

Equality in the triangle inequality holds iff $z_1,z_2$ are positive real multiples of each other (collinear, same direction from origin), so $\arg z_1=\arg z_2 \implies \arg z_1-\arg z_2=0.$

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