If z1 and z2 are two non-zero complex numbers such that |z1+z2| =|z1|+|z2|, then arg ((z1/z2)) is equal to

Question

If z1 and z2 are two non-zero complex numbers such that |z1+z2| =|z1|+|z2|, then arg ((z1/z2)) is equal to (A) 0 (B) -π (C) -(π/2) (D) (π/2)

Tardigrade Admin · Accepted Answer

Given |z1+z2|=|z1|+|z2| We know that |z1+z2| le|z1|+|z2| Equality holds when z1, z2 are collinear with the origin. ⇒ arg((z1/z2))=arg z1- arg z2 =0

Q. If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣$ , then arg $(\frac{z _{1}}{z _{2}})$ is equal to