mycroft holmes
Last Activity: 9 Years ago
Let O be origin, A be z1, B be z2 and C be the point corresponding to z1+z2 on the complex plane. Then OAZB is a rhombus and z1+z2 and z1-z2 are the diagonals.
From geometry we know that the diagonals of a rhombus interesect at right angles.
Hence arg (z1+z2/z1-z2) = 90 deg or – 90 deg i.e z1+z2/z1-z2 is purely imaginary