Complex Theory

Algebra Level pending

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

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