Question

If $z_1,z_2$ are two complex numbers such that $\left|\frac{z_1-z_2}{z_1+z_2}\right|=1$ and $i{z}_1=k{z}_2$ where $k\in R$, the the angle between $z_1-z_2$ and $z_1+z_2$ is

• A. ${\tan }^{-1}\left(\frac{2k}{k^2+1}\right)$
• B. ${\tan }^{-1}\left(\frac{2k}{1-k^2}\right)$
• C. $-2{\tan }^{-1}k$
• D. $2{\tan }^{-1}k$.

Answer 1

Answer: (A), (D)

The correct options are
A ${\tan }^{-1}\left(\frac{2k}{k^2+1}\right)$
D $2{\tan }^{-1}k$.