If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|$ then $\arg z_{1}-\arg z_{2}$ is equal to

JEE Main · 2005 · 08 May 2005 · Offline · Complex Numbers

z_{1}

and

z_{2}

are two non-zero complex numbers such that

∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣

then

ar g z_{1} - ar g z_{2}

is equal to

Answer: (C)

The equality

∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣

is the boundary case of the triangle inequality, and it occurs only when

z_{1}

and

z_{2}

point in the same direction from the origin. Two such complex numbers have equal arguments, so

ar g z_{1} - ar g z_{2} = 0

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option