If  $z=x+iyandrootsofz{\overline{z}}^3+\overline{z}{z}^3=30$  are the  vertices  of a  rectangle  and  $z_0$ is  centre  of  
rectangle.  Let  d  be distance of  $z_0$ from  the point  of  circle $|z-3|\le 2$  then  maximum  value of  d is -------------

 $\Rightarrow z\stackrel{-}{z}(\stackrel{-}{z^2}+z^2)=30$
 $\Rightarrow (x^2+y^2)\left(\right(x^2-y^2)-2ixy+x^2-y^2+2ixy))=0$
 $\Rightarrow (x^2+y^2)\left(\right(x^2-y^2)=15=(2^2+1\left)\right(2^2-1)$
Which suggests the  possible  value  of   x and y  are 
X=2,y=-1
Center of  rectangule is (0,0)
Maximum distance of  (0,0)  from the circle  is 5  and minimum is  1