Question
Question: If z<sub>1</sub> and z<sub>2</sub> are two non-zero complex numbers such that \|z<sub>1</sub> + z<s...
If z1 and z2 are two non-zero complex numbers such that
|z1 + z2| = |z1| + |z2|, then Arg z1 – Arg z2 =
A
– p
B
– p/2
C
0
D
p/2
Answer
0
Explanation
Solution
Sol. |z1 + z2| = |z1| + |z2|
|z1|2 + |z2|2 + 2|z1| |z2| cos (q1 – q2) = |z1|2 + |z2|2 + 2|z1| |z2|
Ž cos (q1 – q2) = 1 Ž q1 – q2 = 00
arg (z1) – arg (z2) = 00