If complex number z lies in the interior or on the boundary of circle of radius 3 units, then maximum and minimum values of |z+1| are

Step-by-step solution

Here, we have Radius of circle =3 units we find the maximum and minimum value of |z+1| for z lying in the interier or boundary of the circle |z|=3 For Max |z+1|, z must lies on the bondary of the circle, then |z|=3 and z=3 e^ , where is the argument of z . Now, |z+1|= |3 e^ i +1 | aligned & =|(3 +1)+(3 i )| & = (3 +1)^2+(3 )^2 aligned aligned & = 9+1+6 & = 10+6 aligned , ranges from -1 to 1 , the maximum value of |z+1| occur, when =1 . Therefore, Max |z+1|= 10+6 = 16 =4 For minimum value The minimum value of z+1 oc