If z1, z2 are complex numbers such that, 2z1/ 3z2 is purely imaginary number, then finds | z1− z2/ z1+ z2|

Question

If z_1, 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

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

\(\frac{z_1}{z_2}\) = \(\frac{3λ}{2}\)i

Now,