Let `A=[(1+i,1),(-i,0)]` then find the total number of elements in the set where `{n in {1,2,3,. . .,100}` and given that `{A^n=A}`

The number of elements in the set {n in {1, 2, 3,…, 100} | (11)^(n) gt (10)^(n) + (9)^(n)} is ________ .

Let s_1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} , s_2 = {(i,j) ∶ 1 ≤ i s_3 = {(i,j, k, l) ∶ 1 ≤ i s_4 = {(i,j, k, l) ∶ i,j, k and l are distinct elements in {1,2, … ,10}} . If the total number of elements in the set s_r is n_r , r= 1,2,3,4, then which of the following statements is (are) TRUE ?

The number of elements of the set {x: X in N,x^(2) = 1} where N is the set of all natural numbers is :

Find the value of sum_(n=0)^(100)i^(n!), where i=sqrt(-1)

Find the lowest value of n such that ((1-i)/(1+i))^(n^(2))=1 , where n in N .

What is the modulus of the complex number i^(2n+1) (-i)^(2n-1) , where n in N and i=sqrt(-1) ?

If sum_(i=1)^(2n)cos^(-1)x_(i)=0 then find the value of sum_(i=1)^(2n)x_(i)

Let f(n) = [(1)/(2) + (n)/(100)] where [n] denotes the integral part of n. Then the value of sum_(n=1)^(100) f(n) is