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ModernLogic

*Let a0, . . . , an be points on the unit circle. Show that there is some other point p on the unit circle such that the product of the distances from p to ai for i=0,...,n at least 1. (Hint: Maximum Modulus Principle)*

Maximum Modulus Principle: Let f be a nonconstant holomorphic function in the open connected subset G of C. Then absolute value of f does not attain a local maximum.

Maximum Modulus Principle: Let f be a nonconstant holomorphic function in the open connected subset G of C. Then absolute value of f does not attain a local maximum.

Man, I'm so stuck on this problem. I can't seem to figure out how the maximum modulus principle relates to the problem. Besides, the problem is asking me to find the lower bound for the product whereas the the maximum modulus principle states that there is no upper bound. I'm so confused.

Anything would help from you geniuses out there: A hint or advice.

Regards,

Steve