be a complex valued rational function.
How can I show that, if , then there is a complex number satisfying and ?
I have tried in many ways, but on success. Basically I tried to show that there is a unimodular complex number such that
I could make a quadratic equation by using the fact that Unfortunately I could not solve this question using that. So, I would like to see different (and somewhat general) approach.
Also, I would like to know that what happen if (both or atleast one) Any comment or hint will be welcome. Thank you.