I am working through some problems in Axler's Linear Algebra Done Right textbook, and I noticed that I haven't really developed an intuitive feel for how to approach existence in the proofs.
The idea of existence just seems very vague to me. For instance, in one of the problems, the book asks you to find real numbers c and d given real numbers a and b in the following expression:
1/(a+bi) = c+di
From what it looks like, if I can express c and d in terms of a and b, that means that c and d exist because a and b are assumed to exist? Is there are more solid way for me to approach existence in proofs?