Find the sum of the 5^th roots of unity.

The 5th roots of unity are the solutions of the equation:

x5=1x^5 = 1

These roots are given by:

ωk=e2πik/5,for k=0,1,2,3,4\omega_k = e^{2\pi i k / 5}, \quad \text{for } k = 0, 1, 2, 3, 4

where ω0=1\omega_0 = 1 is the principal root, and the _______ ____ ______ _____ ___ ______ ________ ________ _____ __________ ______.
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