Home
Class 11
MATHS
Prove that i^(107)+i^(112)+i^(117)+i^(12...

Prove that `i^(107)+i^(112)+i^(117)+i^(122)=0`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise EXERCISE 5.1|13 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise EXERCISE 5.2|8 Videos
  • BINOMIAL THEOREM

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|7 Videos
  • CONIC SECTIONS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|9 Videos

Similar Questions

Explore conceptually related problems

i^(9)+i^(10)-3i^(12)=-4

Find the value of i^(2017)+i^(2018)+i^(2019)+i^(2020) .

Evaluate [i^(18) + (1/i)^(25)]^(3)

If a_(i) gt 0 AA I in N such that prod_(i=1)^(n) a_(i) = 1 , then prove that (a + a_(1)) (1 + a_(2)) (1 + a_(3)) .... (1 + a_(n)) ge 2^(n)

If A=[{:(0,1),(0,0):}]andI=[{:(1,0),(0,1):}] then prove that (aI+bA)^(3)=a^(3)I+3a^(2)bA .

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

Prove that : A^(2)-6A+17I_(2)=0 . When A=[{:(2,-3),(3,4):}] Also find A^(-1) .

Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))

Sum of four consecutive powers of i(iota) is zero. i.e., i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0,forall n in I. If sum_(n=1)^(25)i^(n!)=a+ib, " where " i=sqrt(-1) , then a-b, is

Sum of four consecutive powers of i(iota) is zero. i.e., i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0,forall n in I. If sum_(r=-2)^(95)i^(r)+sum_(r=0)^(50)i^(r!)=a+ib, " where " i=sqrt(-1) , the unit digit of a^(2011)+b^(2012) , is