If `z_1a n dz_2` are two nonzero complex numbers such that =`|z_1+z_2|=|z_1|+|z_2|,` then `a rgz_1-a r g z_2` is equal to `-pi` b. `pi/2` c. `0` d. `pi/2` e. `pi`

Options

A. `-pi`
B. `pi//2`
C. 0
D. `pi//2`

Answer

C

Explanation

Let `z_(1)=r_(1)(costheta_(1)+isintheta_(1)), z_(2)=r_(2)(costheta_(2)+isintheta_(2))`.
Then, `|z_(1)+z_(2)|=|z_(1)|+|z_(2)|`
`rArr r_(1)^(2)+r_(2)^(2)+2r_(1)r_(2)cos(theta_(1)-theta_(2))= r_(1)^(2)+r_(2)^(2)+2r_(1)r_(2)`
`rArr cos(theta_(1)-theta_(2)) = 1 rArr theta_(1)-theta_(2)=0 rArr "arg"(z_(1))-"arg"(z_(2))=0`