Stage: 5 Challenge Level: 
The hint is in the title here!
If $z_1z_2z_3=1$ what can you say about ${1\over z_1} + {1\over z_2} + {1\over z_3}$?
alphas. Surds. Complex numbers. Stage 5 - Reviewed 2012. Quadratic equations. Simultaneous equations. Long problems. Roots of equations and coefficients. Mathematical reasoning & proof. Golden ratio.
Published July 1999.
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