¿Cuál es el valor de i51

?

A.

−1

B.

−i

C.

1

D.

i

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

Hello from MrBillDoesMath!

  x = 4, slope intercept form is y = 2x + 11

Discussion:

A vertical line  goes straight up and down. The only thing "fixed" about it is its x value. Hence a vertical line has an equation like "x = ?". As your line passes through (4, -3), with x value 4. its equation is x = 4.

The slope intercept form of a line is " y = mx + b" where m is the slope of the line and b is its y intercept. We are told the desired line is parallel to  y = 2x -1 which  means both lines have the same slope (which is 2, boldfaced, above). So,  we know the slope intercept form is

y = 2x + b

but we are also told the line passes through (-3,5). Substituting these values in the above equation gives

y = 2x + b

5 = 2 (-3) + b

5 = -6 + b

b = 5 + 6 = 11

The final slope intercept form is y = 2x + 11

Regards, MrB