Question

find the zeros and poles of the function z-9/z²-3z+2
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Answer 1

Answer:

Let h(z)=z6−5z4+3z2−1.

Using Rouche's theorem, with f(z)=−5z4 and g(z)=z6+3z2−1.

On the unit disc |f(z)|=5>|1+3−1|=|g(z)|

And the number of zeros is 4 for f(z) in the unit disc, so it is also five for h(z)=f(z)+g(z).

Is this correct? Thanks.

Found an old answer of mine, I chose g(z)=z6−1 and f(z)=−5z4+3z2, and got the answer 4 roots again.