Question

How do you simplify `i44 + i150 - i74 - i109 + i61`?

Answer 1

1

Explanation:

We have,
`i^1=i`
`i^2= -1`
`i^3 = i^2 xx i = -i`
`i^4 = i^2 xx i^2 =(-1)^2 xx (-1)^2 = 1`
`i^5 = i^4 xx i = 1 xx i =i`
`i^6 = i^4 * i^2 = 1 * -1 = -1`
`i^7 = i^4 * i^3 = 1 * -i = -i`
`i^8 = i^4 * i^4 = 1 * 1 = 1`

Now,
`i^44 = (i^4) ^11 = (1)^11 = 1`
`i^150 = (i^4)^37 * i^2 = i^2 = -1`
`i^74 = (i^4)^18 * i^2 = i^2 = -1`
`i^109 = (i^4)^27 * i^1 = i`
`i^61 = (i^4)^15 * i^1 = i`

Finally,
`i^44 + i^150 - i^74 - i^109 + i^61`
`=(1) + (-1) - (-1) - (i) + (i)`
`=1 - 1 + 1 - i + i`
`= 1`