Question

If arg(z1/z2)=pi/2 then find the value of z1+z2/z1-z2

Answer 1

arg(z1/z2) = π/2
we know, if Z = x + iy is a complex number
then, arg(z) = tan^{-1} y/x

so, arg(z1/z2) = π/2 means to say, real part of (z1/z2) is zero.
let , z1/z2 = ia
so, z1 = ia.z2 .......(1)


now, |z1- z2|/|z1 - z2| = |iaz2 + z2|/|iaz2 - z2|

= |ia + 1|/|ia + 1 |

= √{a² + 1²}/√{(-a)² + 1²}

= 1

hence the value of |z1 + z2|/|z1 + z2| = 1