Qn 3: I think you meant, the lines joining z1 and z2 are perpendicular.
Consider triangle OZ1Z2 right angled at Z1.
By Pythagoras theorem (Z1Z2)2 = OZ12 + OZ22
Now OZ1 = |z1|; OZ2 = |z2| and Z1Z2 = |z1-z2|
Hence |z1|2+|z2|2 = |z1-z2|2 = (z1-z2) (z'1-z2') = |z1|2+|z2|2 - (z1z2' +z1'z2)
Hence z1z2' +z1'z2 = 0.
Moderation Team
![[Post New]](/templates/default/images/icon_minipost_new.gif){kind=icon}
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
926
