For any integer k , let alphak=cos(kpi)/...

For any integer `k ,` let `alpha_k=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt(-1)dot` Value of the expression `(sumk=1 12|alpha_(k+1)-alpha_k|)/(sumk=1 3|alpha_(4k-1)-alpha_(4k-2)|)` is

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
CIRCLES
VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

For any integer k , let alpha_k=cos((kpi)/7)+isin((kpi)/7),w h e r e i=sqrt(-1)dot Value of the expression (sum_(k=1)^(12)|alpha_(k+1)-alpha_k|)/(sum_(k=1)^3|alpha_(4k-1)-alpha_(4k-2)|) is

The real value of alpha for which the expression (1- isin alpha)/(1+2i sinalpha) is purely real is

Let z_(k) = cos((2kpi)/(10)) -isin ((2kpi)/(10)), k = 1,2,…..,9

Let z_(k)=cos((2kpi)/(10))+isin((2kpi)/(10)) ,k=1,2,…,9. Then match the column

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If (2 sin alpha)/(1 + cos alpha + sin alpha) = 3/4 , then the value of (1 - cos alpha + sinalpha)/(1 + sin alpha) is equal to

let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4)) be an identity in x, where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are independent of x. Then find the value of alpha_(1)alpha_(2)alpha_(3)alpha_(4)

Let z_(k)=cos(2kpi)/10+isin(2kpi)/10,k=1,2,………..,9 . Then, 1/10{|1-z_(1)||1-z_(2)|……|1-z_(9)|} equals

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE

Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...
Text Solution
|
The quadratic equation p(x)=0 with real coefficients has purely imagin...
Text Solution
|
For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...
Text Solution
|
Let a,b,x and y be real numbers such that a-b =1 and y ne 0. If the ...
Text Solution
|
If z(1)=p+iq and z(2) = u = iv are complex numbers such that |z(1)|=...
Text Solution
|
Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...
Text Solution
|
Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...
Text Solution
|
about to only mathematics
Text Solution
|
Find the centre and radius of the circle formed by all the points repr...
Text Solution
|
If one of the vertices of the square circumscribing the circle abs(z-1...
Text Solution
|
Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...
Text Solution
|
If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...
Text Solution
|
If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...
Text Solution
|
Express 1//(1-costheta+2isintheta) in the form x=i y .
Text Solution
|
If n is n odd integer that is greater than or equal to 3 but not a mul...
Text Solution
|
The real values of xa n dy for which the following equation is satisfi...
Text Solution
|
Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...
Text Solution
|
A relation R on set of complex numbers defined by Z(1)RZ(2) hArr (Z(1)...
Text Solution
|
Prove that the complex numbers z(1),z(2) and the origin form an equ...
Text Solution
|
If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...
Text Solution
|