sum(k=1)^10(sin(2kpi)/11+icos(2kpi)/11)...

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

`-i`

-1

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos
COMPLEX NUMBERS
MCGROW HILL PUBLICATION|Exercise EXERCISE NUMERICAL ANSWER TYPE QUESTIONS|20 Videos
CIRCLES AND SYSTEMS OF CIRCLES
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos
DEFINITE INTEGRALS
MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

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"):}

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS

If w = z/(z-1/3i) and |w| =1, then z lies on
Text Solution
|
If z1 and z2, are two non-zero complex numbers such that |z1+z2|=|z1|...
Text Solution
|
sum(k=1)^10(sin(2kpi)/11+icos(2kpi)/11)
Text Solution
|
If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...
Text Solution
|
If |z""+""4|lt=3 , then the maximum value of |z""+""1| is (1) 4...
Text Solution
|
The conjugate of a complex number is 1/(i-1) . Then the complex num...
Text Solution
|
If |z-4/z| = 2 , then the maximum value of |z|
Text Solution
|
The number of complex numbers z such that |z-1|=|z+1|=|z-i| is
Text Solution
|
If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...
Text Solution
|
Let alpha,beta be real and z be a complex number. If z^2+alphaz""+beta...
Text Solution
|
If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...
Text Solution
|
The area of the triangle on the Arand plane formed by the complex numb...
Text Solution
|
If z is a complex number of unit modulus of modulus and argument thet...
Text Solution
|
if (5z2)/(7z1) is purely imaginary number then |(2z1+3z2)/(2z1-3z2) |...
Text Solution
|
Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...
Text Solution
|
If a complex number z satisfies z + sqrt(2) |z + 1| + i=0, then |z| is...
Text Solution
|
If z is a complex number such that |z|>=2 then the minimum value of |z...
Text Solution
|
Let w(Im w != 0) be a complex number. Then the set of all complex num...
Text Solution
|
If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...
Text Solution
|
Let z!=i be any complex number such that (z-i)/(z+i) is a purely imagi...
Text Solution
|