Bissoy.com
Doctors Medicines MCQs Q&A

If m, n, p, q are consecutive integers then the value of iminipiq is

If m, n, p, q are consecutive integers then the value of iminipiq is Correct Answer None of these

Concept:

i2 = -1

Calculation:

∵ m, n, p and q are consecutive integers and let us suppose m be the first integer, then we can express other integers as n = m + 1, p = m + 2 and q = m + 3.

⇒ im × in × ip × iq = i(m + n + p + q)    (∵ ax × ay = a(x + y))

⇒ im × in × ip × iq = i(m + (m + 1) + (m + 2) + (m + 3))   (By expressing the integers n, p and q in terms of m)

⇒ im × in × ip × iq = i(4m + 6)

⇒ im × in × ip × iq = i4m × i6    

⇒ im × in × ip × iq = -i4m   (∵ i6 = -1)

⇒ im × in × ip × iq = -1     (∵ i4m = 1, ∀ m ∈ Z)

Related Questions

Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?
If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is :
If the average of 7 consecutive positive odd integers is P. Then what is the average of next seven consecutive off integers in terms of P?
If the average of 5 consecutive integers is x then, find the average of next to next 5 consecutive integers.
A, B, C, D and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 4. D is the greatest and A is the least. B is greater than E but less than C. The sum of the integers is equal to E. What is the positive difference between the lowest and the highest integers?
The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers ?
In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers ?
In a sequence of consecutive integers, how much greater is the sum of the last four integers than sum of first four integers?
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
In ascending order, three consecutive integers are placed in a way that sum of last two integers is 13 more than the first integer. What are three possible integers?