Establish the following minimum modulus principle.
((a)) Let f be analytic and nonconstant in the domain D, and continuous on the closed region R that consists of D and all its boundary points B. Show that, if f(z)=0 throughout R, then ∣f(z)∣ assumes its minimum value, but does so only at point(s) z0 on the boundary B.
((b)) Show that the requirement f(z)=0 in part (a) is necessary by finding a function for which the requirement fails, and whose minimum modulus is attained at some place other than the boundary.