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complex equation, counting signs

Source: Yugoslav TST 1972 P1

May 30, 2021
algebracomplex numbers

Problem Statement

Given non-zero real numbers u,v,w,x,y,zu,v,w,x,y,z, how many different possibilities are there for the signs of these numbers if (u+ix)(v+iy)(w+iz)=i?(u+ix)(v+iy)(w+iz)=i?
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