¿Cuál es el valor de i51?


A.


−1


B.


−i


C.


1


D.


i


Answer: Option B.

Step-by-step explanation:

We want to find the value of i^51

We know that

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

and it repeats with a period of 4, so i^5 = i^(1 + 4) = i^1= i, and so on.

so we can write it as:

x + n*4 = 51

where n is an integer number, and x is a number between 1 and 4.

clearly  n must be an odd number, so we can try:

if x = 1.

1 + n*4 = 51

n*4 = 50

n = 50/4 = 12.5

This is not the solution for x, because n must be an integer number.

Now suppose x = 3.

3 + 4*n = 51

4*n = 48

n = 48/4 = 12

Then x is equal to 3, this means that:

i^51 = i^3*i^4*12 = i^3 = -i

The correct option is B


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