Help me please with this one:
Locate the zeros of
and show that they are simple
If it is compulsory to apply Rouche's theorem as title says, then, for all such that :
According to Rouche's theorem, the number of zeros of in including multiplicities is equal to the number of zeros of in . That is, .
Tonio's hint for the restriction of to allows to locate those two zeros and prove that both are simple.