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If two non-zero complex numbers z1 and z2 satisfy |z1 + z2| = |z1| + |z2|, then the value of arg z1 - arg z2 is

1. π/2
2. -π
3. 0
4. -π/2

Correct answer: 0

Solution

The triangle-inequality becomes an equality only when z1 and z2 point in the same direction, i.e. they have equal arguments. Therefore arg z1 - arg z2 = 0.

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