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## Homework Statement

It is known that roots of complex polynomial:

##P_n (z) = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0##

are the following complex numbers:

##\alpha_1, \alpha_2, \cdots, \alpha_n ##

Find the product:

##\prod = (\alpha_1 + 1)(\alpha_2 + 1)\cdots(\alpha_n +1)##

## Homework Equations

## The Attempt at a Solution

I am pretty sure that i have to use Vieta formulas somehow, and since roots are all complex then it means that there are n/2 pairs of complex-complex conjugate roots. If i multiply all of this i would end up with product of all roots ##\alpha_1* \alpha_2* \cdots* \alpha_n ## and by Vieta formulas i can easily determine that one, but there are more elements of this product after multiplying, what can i do with them?