Let z1 and z2 be non-zero complex numbers satisfying the equation z1 2−2z1z2+2z22=20 , the geometrical nature of the triangle whose vertices are the origin and the points representing z1  and  z2 is

The given equation is z1 2−2z1z2+2z2 2=0 ⇒(z1z2)2−2(z1z2)+2=0⇒z1z2=2±4−82=(1±i)   ⇒ z1=1±iz2⇒|z1|=2  |z2|.................(1)again,z1=z2±iz2⇒z1−z2=±iz2             ⇒(z1−z2)  is   ⊥to   z2 …………..(2)             [ since arg z1-z2 = arg ±iz2  = arg ±i +arg z2 =±π2 +arg z2        ⇒   arg z1-z2-argz2 =±π2]          and  |z1−z2|=|z2| ⇒ z1-z2=0-z2⇒O,z1   and  z2  from an isosceles right angled triangle.