Let A,B  and C  represent the complex numbers z1,z2,z3  respectively on the complex plane. if the circumcentre of the triangle A,B,C  lies at the origin, then the nine point centre is represented by the complex number:

Circumcentre =0, centroid =z1+z2+z33 Let orthocentre by γ .∴             z1+z2+z33=1.γ+202+1 ∴             γ=z1+z2+z3 But nine point centre is the midpoint of orthocentre and circumcentre.∴  Nine point centre =γ+02=z1+z2+z32 .