MathDB

Let

z=x+iy

be a complex number with

x

and

y

rational and with

|z| = 1.

(a) Find two such complex numbers. (b) Show that

|z^{2n}-1|=2|\sin n\theta|,

where

z=e^{i\theta}.

|z^2n -1|

is rational for every

n.

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