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If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 – argz2 is equal to ?

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 – argz2 is equal to ?

Grade:12

2 Answers

Latika Leekha
askIITians Faculty 165 Points
6 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
raghavendra
36 Points
3 years ago
|Z1+Z2|=|Z1|+|Z2|. So Z1 , Z2, Z1+Z2 are collinear.they are lies on same line. so angle between them is zero.

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