(2) Let ωn := e2πi/n for n = 2,3,.... (a) Show that the n’th roots of...

(2) Let ωn := e2πi/n for n = 2,3,....

(a) Show that the n’th roots of unity (i.e. the solutions to zn = 1) are

ωnk fork=0,1,...,n−1.
(b) Show that these sum to zero, i.e.

1+ω +ω2 +···+ωn−1 =0.nnn
(c) Let z◦ = r◦eiθ◦ be a given non-zero complex number. Show that the n’th roots of z◦ are

c◦ωnk fork=0,1,...,n−1 where c◦ := √n r◦eiθ◦/n.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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