It is given, for a complex number Z=x+iy, where x,y are integers such that ZZ3+Z(Z)3=350 ⇒ZZ(Z2+(z)2)=350
⇒(x2+y2)2(x2−y2)=350[∴ZZ=|z|2]
⇒(x2+y2)(x2−y2)=175 ∴x2+y2=25 and x2−y2=7[∵x,y∈ Integer ] So, x2=16 and y2=9 Therefore vertices of the rectangle are (±4,±3),xso area of the rectangle is 4×4×3=48.