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

8 years ago

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 Kushagra Madhukar
11 months ago
Dear student,

given a=e^i(8*pi/11)
aply 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) / (sin pi/11) = =   (cos12pi/11)/( 2 sin pi/11) = – ½

Thanks and regards,
Kushagra