I am self studying complex analysis and came across this question. What are invariant sets under magnification M(z) = az, a>0. The author doesn't state this but I'm assuming a is Real, otherwise we're talking about possible rotation.
I'm thinking possibly 0, the entire complex plane, and any line in the complex plane?
Which also made me wonder about the same in real analysis, is the set of Real numbers invariant under scale since they are infinite and for any number I choose there is another number between that number and zero?