Question

How do I find all seventh roots of unity?

Answer 1

\[z^n=1={\large e^{0i}}=\cos0+i\sin0\]
One obvious root would be \(z_1=1\). The other 6 roots will have the form
\[\cos\left(\frac{0+2k\pi}{n}\right)+i\sin\left(\frac{0+2k\pi}{n}\right)\]
where \(k=1,2,3,4,5,6\).