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Let 21, 22,..., 21011 be complex numbers such that 2₁ +22+...+ 21011 = 0 and |21| = |22| = = |21011| = = 1. Prove that |1 + 21|² + |1 + z2|² + + |1 + ²1011|² = 2022.

Let 21, 22,..., 21011 be complex numbers such that 2₁ +22+...+ 21011 = 0 and |21| = |22| = = |21011| = = 1. Prove that |1 + 21|² + |1 + z2|² + + |1 + ²1011|² = 2022.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Let 21, 22,..., 21011 be complex numbers such that 2₁ +22 + ... + 21011 = 0 and |21| = |22| = = |21011| = 1. Prove that |1+z1|² + |1 + z2|² + ... + |1 + 21011|² = 2022.
Transcribed Image Text:Let 21, 22,..., 21011 be complex numbers such that 2₁ +22 + ... + 21011 = 0 and |21| = |22| = = |21011| = 1. Prove that |1+z1|² + |1 + z2|² + ... + |1 + 21011|² = 2022.
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