If z1, z2 are complex numbers such that, 2z13z12z13z1is purely imaginary number, then finds |z1−z2z1+z2z1−z2z1+z2 |

Question

If z1, z2 are complex numbers such that,\(\frac{2z_1}{3z_1}\) is purely imaginary number, then finds  \(|\frac{z_1-z_2}{z_1+z_2}|\) 

 

Answer 1

since , \(\frac{2z_1}{3z_1}\)  is purely imaginary 

\(\frac{2z_1}{3z_1} \) ==\(\lambda\)  for some \(\lambda ∈ R\)  

\({z_1\over z_2}={ 3 \lambda \over2}i\) 

Now ,