prove that :
on c where C: the line segment from z=i to z=1
where M is an upper bound of on C and L is the length of C.
the length of C is
where z is the distance from a point on C to the origin
To maximize we have to minimize
The shortest distance from a point on C to the origin is . (It's the length of the perpendicular bisector of C.)
so
which implies that
then