The discussion centers on solving a complex numbers problem involving three complex numbers Z1, Z2, and Z3, where Z1 + Z2 + Z3 = 0 and Z1*Z2 + Z2*Z3 + Z3*Z1 = 0. Participants emphasize the necessity of showing work to identify potential errors in the solution process. The problem requires calculating the expression (|z1| + |z2| + |z3|) / (|z1*z2| + |z2*z3| + |z3*z1|), but attempts to manipulate the equations using conjugates have proven unfruitful.
PREREQUISITESStudents studying complex analysis, mathematicians tackling algebraic equations, and anyone interested in advanced problem-solving techniques involving complex numbers.
Keiner Nichts said:Homework Statement
If Z1+Z2+Z3=0 and Z1*Z2 + Z2*Z3 + Z3*Z1=0 and Z1, Z2, Z3 are all complex, what is the value of
(|z1|+|z2|+|z3|)/(|z1*z2|+|z2*z3|+|z3*z1|)
Homework Equations
The Attempt at a Solution
I tried to multiply the equations by the product of all conjugates and reach some equations but it lead to nothing in the end.[/B]