# the blue rectangle is the source in the z-plane,
# the red shape is the image in the w-plane
with(plots):
F:=1/z; # the function
LLx:=1: # Lower Left Coordinates
LLy:=1:
URx:=2: # Upper Right Coordinates
URy:=2:
RM:=max(abs(LLx),abs(LLy),abs(URx),abs(URy)):
# the image of the four corners.
LLc:=eval(F,z=LLx+I*LLy):
LRc:=eval(F,z=URx+I*LLy):
URc:=eval(F,z=URx+I*URy):
ULc:=eval(F,z=LLx+I*URy):
FM1:=max(abs(Re(LLc)),abs(Re(LRc)),abs(Re(URc)),abs(Re(ULc))):
FM2:=max(abs(Im(LLc)),abs(Im(LRc)),abs(Im(URc)),abs(Im(ULc))):
M:=max(RM,FM1,FM2): # M is big enough to see everything
# A is the source
A:=conformal(z,z=LLx+I*LLy..URx+I*URy,-M-I*M..M+I*M,color=blue):
# B is the image
B:=conformal(F,z=LLx+I*LLy..URx+I*URy,-M-I*M..M+I*M,color=red):
# show then together
display(A,B);