Question

If z1 and z2 are two non-zero complex number such that |z1+z2|= |z1| + |z2| ,then what is value of argz1-argz2 ?

Answer 1

`argz_1-argz_2=0`

Explanation:

`z_1` and `z_2` are two complex number. We can represent sum of complex numbers as a diagonal of the parallelogram formed by them as shown in the figure below. Further, absolute of a complex number is represented by its distance from origin or the length of the vector.

Observe that if arguments of two complex numbers are different then they form a parallelogram and `|z_1+z_2|<|z_1|+|z_2|`.

When we will have`|z_1+z_2|=|z_1|+|z_2|`? It will be when the two vectors are completely aligned i.e.

`argz_1=argz_2` or `argz_1-argz_2=0`