`sum_(k=1)^10(sin(2kpi)/11+icos(2kpi)/11)`

The value of sum_(n=1)^(10) {sin(2npi)/11-icos(2npi)/11} , is

Find the value of sum_(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wherei=sqrt(-1).

The value of sum_(k=1)^(10)((sin(2 pi k))/(11)-i(cos(2 pi k))/(11)) is

If p=sum_(p=1)^(32)(3p+2)(sum_(q=1)^(10)(sin""(2qpi)/(11)-icos""(2qpi)/(11)))^(p) , where i=sqrt(-1) and if (1+i)P=n(n!),n in N, then the value of n is

The value of sum_(r=1)^(8)(sin(2rpi)/9+icos(2rpi)/9) , is

If S=underset(k=1) overset(10)sum(sin""(2pik)/11-icos""(2pik)/11) then

sum_ (k = 1) ^ (10) ((sin (2k pi)) / (11) + i (cos (2k pi)) / (11))

Match the following : {:("Column-I" ," Column-II"),("(A) The value of " underset(k=1)overset(2007)sum (sin""(2kpi)/9 - icos""(2kpi)/9) " is" , " (p) -1"),("(B) If " z_(1)","z_(2) and z_(3) " are unimodular complex numbers such that " |z_(1)+z_(2)+z_(3)|=1 " then " |1/z_(1)+1/z_(2) + 1/z_(3)| " is equal to " , " (q) 2 "),("(C) If the complex numbers " z_(1)"," z_(2) and z_(3) " represent the vetices of an equilateral triangle such that " |z_(1)|=|z_(2)|=|z_(3)| " then " (z_(1) +z_(2) +z_(3)) -1 " is equal to " , " (r) 1"),("(D) If " alpha " is an imaginary fifth root of unity , then " 4log_(4)| 1+alpha +alpha^(2) +alpha^(3) -1/alpha| " is " , " (s) 0"):}