Let a(n)=i^((n+1)^2), where i=sqrt(-1)" ...

Let `a_(n)=i^((n+1)^2)`, where `i=sqrt(-1)" and "n=1, 2, 3,"……….."`. Then the value of `a_(1)+a_(3)+a_(5)+"……….."+a_(25)` is

`13`

`13+i`

`13-i`

`12`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
BINOMIAL THEOREM
NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
CONIC SECTIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If a_(1)=-1 and a_(n)=(a_(n-1))/(n+2) then the value of a_(4) is ____.

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to

If the sequence a_(1),a_(2),a_(3) ,…….. Is an A.P., then the sequence a_(5), a_(10), a_(15) ,…….. Is ………..

If a_(1) = 4 and a_(n + 1) = a_(n) + 4n for n gt= 1 , then the value of a_(100) is

If (1+x+x^(2))^(20) = a_(0) + a_(1)x^(2) "……" + a_(40)x^(40) , then following questions. The value of a_(0) + a_(1) + a_(2) + "……" + a_(19) is

If a_(1), a_(2) , ……. A_(n) are in H.P., then the expression a_(1)a_(2) + a_(2)a_(3) + ….. + a_(n - 1)a_(n) is equal to

If a_(1), a_(2), a_(3), ......... , are in A.P. with common difference 5 and if a_(i)a_(j) != - 1 for i ,j = 1, 2, .... , n , then tan^(1)(5/(1 + a_(1) a_(2))) + tan ^(1)(5/(1 + a_(2)a_(3))) + ...... + tan^(-1)(5/(1 + a_(n - 1)a_(n))) is equal to

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is

Given a_(1)cos alpha_(1)+alpha_(2)cos alpha_(2)+…+a_(n)cos alpha_(n)=0 and a_(1)cos(alpha_(1)+theta)+a_(2)cos(alpha_(2)+theta)+…+a_(n)cos(alpha_(n)+theta)=0 (theta ne k pi) , then the value of a_(1)cos(alpha_(1)+lambda)+a_(2)cos(alpha_(2)+lambda)+…+a_(n)cos(alpha_(n)+lambda) is

Let a_(0)=0 and a_(n)=3a_(n-1)+1 for n ge 1 . Then the remainder obtained dividing a_(2010) by 11 is

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS

If alpha, beta are the roots of the equation x^(2)-px+q=0, prove that ...
Text Solution
|
If sec alpha" and cosec "alpha are the roots of the equation x^(2)-px+...
Text Solution
|
Let a(n)=i^((n+1)^2), where i=sqrt(-1)" and "n=1, 2, 3,"………..". Then t...
Text Solution
|
If (5z2)/(11z1) is purely imaginary, then the value of |(2z(1)+3z(2))/...
Text Solution
|
If 2alpha= -1-isqrt(3)" and"2beta= -1+isqrt(3), then 5alpha^(4)+5beta^...
Text Solution
|
If (i^(4)+i^(9)+i^(16))/(2-i^(8)+i^(10)+i^(3))=a +ib, then (a,b) is
Text Solution
|
If (sqrt(5)+sqrt(3)i)^(33)= 2^(49)z, then modulus of the complex numbe...
Text Solution
|
If a is positive and if A and G are the arithmetic mean and the geomet...
Text Solution
|
Suppose that two persons A and B solve the equation x^(2)+ax+b=0. Whil...
Text Solution
|
If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...
Text Solution
|
If sec theta" and "tan theta are the roots of ax^(2)+bx+c=0 (a,b ne 0)...
Text Solution
|
If the area of the triangle formed by the points z, z+iz and iz is 50 ...
Text Solution
|
The locus of z such that arg[(1-2i)z-2+5i]= (pi)/(4) is a
Text Solution
|
If z= sqrt(3)+i, then the argument of z^(2)e^(z-i) is equal to
Text Solution
|
If omega ne 1" and "omega^(3)=1, the (a omega+b + c omega^(2))/(a omeg...
Text Solution
|
The centre of a regular hexagon is at the point z=i. If one of its ver...
Text Solution
|
If the roots of the equation (1)/(x+p)+(1)/(x+q)=(1)/(r ),(x ne -p, x ...
Text Solution
|
The solution of the equation (3+2sqrt(2))^(x^(2)-8)+(3+2sqrt(2))^(8-x^...
Text Solution
|
If -2-i is a root of the equation ax^(2)+12x+b=0 (where a and b are re...
Text Solution
|
If one root of the equation lx^(2)+mx+n=0" is "(9)/(2) (l,m and n are ...
Text Solution
|