the points abc and d represent the numbers z1z2z3

Question

The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z4.ABCD is rhombus;AC=2BD.if  Z2=2+i ,Z4=1-2i,find Z1 and Z3

Ans) B(2,1) , D(1,-2)

Mid Point (3/2,-1/2)

Write Equation of CD in symmetric form

(x-3/2)/-1/3 = (y+1/2)/-1/3 = r

here r= +(10)^1/2 , -(10)^1/2

 A = 3/2 - ((10)^1/2)/3

D = -1/2 + ((10)^1/2)/3