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# Roots of Unity Questions

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1. Let R be the set of primitive 42nd roots of unity, and let S be the set of primitive 70th roots of unity. How many elements do R and S have in common?

2. Let u,v be distinct complex numbers. If u^2=v and v^2=u, what is uv?

3. If z^3 = 1 and z cannot equal 1, then compute (1-z+z^2)(1+z-z^2).

4. Let $$\omega$$ be a complex number such that $$\omega^5 = 1$$ and $$\omega \neq 1$$. Compute $$\frac{\omega}{1 + \omega^2} + \frac{\omega^2}{1 + \omega^4} + \frac{\omega^3}{1 + \omega} + \frac{\omega^4}{1 + \omega^3}$$.

any help would be appreciated!

Jan 18, 2020
edited by somebody  Jan 18, 2020