with(plots):
F:=1/z; # the function
r0:=1: # Min and Max radius r0 < r1
r1:=2:
a0:=Pi/6: # Min and Max Angles a0 < a1
a1:=Pi/3:
# for conformal range
LLx:=ln(r0):
LLy:=a0:
URx:=ln(r1):
URy:=a1:
RM:=max(abs(r1*cos(a0)),abs(r1*sin(a0)),abs(r1*cos(a1)),abs(r1*sin(a1))):
LLc:=eval(F,z=r0*exp(I*a0)):
LRc:=eval(F,z=r0*exp(I*a1)):
ULc:=eval(F,z=r1*exp(I*a0)):
URc:=eval(F,z=r1*exp(I*a1)):
FM1:=max(abs(Re(LLc)),abs(Re(LRc)),abs(Re(ULc)),abs(Re(URc))):
FM2:=max(abs(Im(LLc)),abs(Im(LRc)),abs(Im(ULc)),abs(Im(URc))):
M:=max(RM,FM1,FM2):
FE:=eval(F,z=exp(z)):
A:=conformal(exp(z),z=LLx+I*LLy..URx+I*URy,-M-I*M..M+I*M,color=blue):
B:=conformal(FE,z=LLx+I*LLy..URx+I*URy,-M-I*M..M+I*M,color=red):
display(A,B);