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  3. (2) let ?n := e2?i/n for n = 2,3,.... (a) show t

(2) Let ?n := e2?i/n for n = 2,3,.... (a) Show that the n’th roots of...

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Advance Math

(2) Let ?n := e2?i/n for n = 2,3,....

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

    ?nk fork=0,1,...,n?1.

  2. (b) Show that these sum to zero, i.e.

    1+? +?2 +···+?n?1 =0.nnn

  3. (c) Let z? = r?ei?? be a given non-zero complex number. Showthat the n’th roots of z? are

    c??nk fork=0,1,...,n?1 where c? := ?n r?ei??/n.

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