Latika Leekha
Last Activity: 10 Years ago
It is given that z1 and z2 are two non-zero complex numbers such that
|z1 + z2| = |z1| + |z2|
On squaring both sides of this equation we get
|z1|2 + |z2|2 + 2|z1| |z2| cos (arg z1 – arg z2) = |z1|2 + |z2|2 + 2|z1| |z2|
This gives 2|z1| |z2| cos (arg z1 – arg z2) = 2|z1| |z2|
Hence, cos (arg z1 – arg z2) = 1
Hence, arg (z1) – arg (z2) = 0.
This is the required answer.
Thanks & Regards
Latika Leekha
askIITians Faculty
