Question

How to prove a no. Has no zeroes

Answer 1

Answer:

heya mate here is your answer ..

Step-by-step explanation:

I am trying to solve the following question:

Let f:C→C,f∈C(C)f:C→C,f∈C(C) and f∈Hol(D)f∈Hol(D) (the unit disk). f≠0f≠0 for every |z|≥1|z|≥1 and f(z)→1f(z)→1 as z→∞z→∞. Show that ff has no zeros in DD.

I was thinking about using the argument principle by showing that for large enough RR, the winding number of f∘Re2πitf∘Re2πit around 0 must be 0, but for that I need f∈Hol(C)f∈Hol(C).

Anyone has another idea?

Thanks!

plzz mark brainliest !!!