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complex sequence z_n = (1+i)(2+i)...(n+i)

Source: Romania BMO TST 1993 p1

February 17, 2020
compexSequencealgebra

Problem Statement

Consider the sequence zn=(1+i)(2+i)...(n+i)z_n = (1+i)(2+i)...(n+i). Prove that the sequence ImIm znz_n contains infinitely many positive and infinitely many negative numbers.
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