Let z be a complex number such that |z|=1 . If 2+ k ^2 z k + z = kz , k R , then the maximum distance of k + ik ^2 from the circle | z -(1+2 i )|=1 is:

Step-by-step solution

aligned & 2+ k ^2 z k + z = kz & | z |^2 k =2 & k =2 aligned point p (2,4) ; center (1,2) distance from circle (x-1)^2+(y-2)^2=1 is max. if ( OP + r )= 1+4 +1= 5 +1