Find the sixth roots of unity, giving your answers in exponential form. If the root with the smalles

Question

Find the sixth roots of unity, giving your answers in exponential form. If the root with the smallest positive argument is denoted by $\omega$, show that $1+\omega+\omega^2+\omega^3+\omega^4+\omega^5=0$.

Accepted Answer

(a) $\left\{e^{i0},e^{i\pi/3},e^{-i\pi/3},e^{i2\pi/3},e^{-i2\pi/3},e^{i\pi}\right\}$ (b) Shown; $1+\omega+\omega^2+\omega^3+\omega^4+\omega^5=0$

Sixth roots of unity

Sixth roots of unity

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