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minachi12

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(e^ix)-1=(2ie^(ix/2))x(sin (x/2))

Calculate this sum

Zn=1+e^(ix)+e^(2ix)+...+e^((n-1)ix)

And deduce those values :

Xn=1+cos(x)+cos(2x)+...+cos((n-1)x)

Yn=sin(x)+sin(2x)+...+sin((n-1)x)