Question

If $z_1$ and$z_2$ are two non-zero complex numbers such that $|z_1+z_2|=|z_1|+|z_2|$ then arg$z_1-$arg$z_2$ is equal to

• A. $\frac{\pi }{2}$
• B. $-\pi$
• C. $0$
• D. $-\frac{\pi }{2}$

Answer 1

Answer: (C)

$0$

$|z_1+z_2{|}^2=|z_1{|}^2+|z_2{|}^2+2|z_1|z_2|$

$\Rightarrow |z_1{|}^2+|z_2{|}^2+2|z_1||z_2|\cos \theta =|z_1{|}^2+|z_2{|}^2+2|z_1||z_2|$

where theta is the angle between $z_1$ and $z_2$. Then,

$\cos \theta =1$

Hence, option C is correct.