If for complex numbers z1 and z2, arg(z1) - arg(z2) = 0, then |z1- z2| is equal to

Question

If for complex numbers z1 and z2, arg(z1) - arg(z2) = 0, then |z1- z2| is equal to (A) |Z1|+|Z2| (B) |Z1|-|Z2| (C) ||Z1|-|Z2|| (D) 0

Tardigrade Admin · Accepted Answer

We have, |z1- z2|2 = |z1|2 + |z2|2 - 2|z1| |z2| cos (θ1 - θ2) where θ1= arg (Z1) and θ2 = arg (z2). Given, arg (z1, - z2) = 0 ⇒ |z1,- z2|2 = |z1|2 + |z2|2 -2 |z1| |z2| = (|z1|-|z1|)2 ⇒ |z1,-z2| = ||z1|-|z2||.

Q. If for complex numbers $z_{1}$ and $z_{2},$ arg $(z_{1})$ - arg $(z_{2}) = 0,$
then $∣ z_{1} - z_{2} ∣$ is equal to

$∣ Z_{1} ∣ + ∣ Z_{2} ∣$

$∣ Z_{1} ∣ - ∣ Z_{2} ∣$

$∣∣ Z_{1} ∣ - ∣ Z_{2} ∣∣$

$0$

Q. If for complex numbers z1​ and z2​, arg(z1​) - arg(z2​)=0, then ∣z1​−z2​∣ is equal to

∣Z1​∣+∣Z2​∣

∣Z1​∣−∣Z2​∣

∣∣Z1​∣−∣Z2​∣∣

0

Q. If for complex numbers $z_{1}$ and $z_{2},$ arg $(z_{1})$ - arg $(z_{2}) = 0,$
then $∣ z_{1} - z_{2} ∣$ is equal to

$∣ Z_{1} ∣ + ∣ Z_{2} ∣$

$∣ Z_{1} ∣ - ∣ Z_{2} ∣$

$∣∣ Z_{1} ∣ - ∣ Z_{2} ∣∣$

$0$