Complex Theory

Algebra Level pending

Consider three different complex numbers z 1 , z 2 , z 3 C z_{1}, z_{2}, z_{3} \in \mathbb{C} . Given that the magnitude of any of those complex numbers is 1 and z 1 + z 2 + z 3 = 1 z_{1}+ z_{2}+z_{3}=1 , find the value of the expression ( 1 z 1 ) ( 1 z 2 ) ( 1 z 3 ) (1-z_{1})(1-z_{2})(1-z_{3})


The answer is 0.

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