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6 Consider the circle K = {z EC: |z| = 3} and n points a1, ..., an EK (n > 1). Show that there exists a point z E K with the property that the product of the distances between z and a; (1 < j < n) is greater than 3".

6 Consider the circle K = {z EC: |z| = 3} and n points a1, ..., an EK (n > 1). Show that there exists a point z E K with the property that the product of the distances between z and a; (1 < j < n) is greater than 3".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6 Consider the circle K = {z EC : |z| = 3} and n points a1, .., an E K (n > 1). Show that there exists a point z EK with the property that the product of the distances between z and a; (1 < j< n) is greater than 3". Hint : use a well-known theorem about holomorphic functions.
Transcribed Image Text:6 Consider the circle K = {z EC : |z| = 3} and n points a1, .., an E K (n > 1). Show that there exists a point z EK with the property that the product of the distances between z and a; (1 < j< n) is greater than 3". Hint : use a well-known theorem about holomorphic functions.
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