If a= e^i(8*pi/11) then find Re(a+a^2+a^3+a^4+a^5).

a+2a

given a=e^i(8*pi/11)
aplly a^2=e^i(16*pi/11)...and so on..
the ans will come on addition...cos 2pi/11 + cos 4pi/11 +..............cos 10pi/11
now apply the formula for summation of angles in Ap..we get,
cos 6pi/11 . sin 5pi/11
_________________ =   cos12pi/11
      sin pi/11                    _________  =  -1/2 (ANS)
                                         2 sin pi/11

Approved

i think the ans is -cos(pi/11)