CPM Homework Help : A2C Problem 9-92

i⁰ = 1 Can you see the pattern?

i¹ = i

i² = −1

i³ = (i)(i²) = −i

i⁴ = (i²)(i²) = 1

i⁵ = (i²)(i²)(i) = i

Hint (a):

The pattern repeats 1, i, −1, and −i

Answer (a):

16 is a multiple of 4.
25 is on more than a multiple of 4.
39 is one less than a multiple of 4.
100 is a multiple of 4.

Hint (b):

i¹⁶ = 1
i²⁵ = i
i³⁹ = −i
i¹⁰⁰ = 1

Answer (b):

Hint (c):

4n is a multiple of 4.

Hint (d):

Refer to (a), (b), and (c).

Hint (e):

i³⁹⁶ = i^4·99 = 1

i³⁹⁷ = i^4·99+1 = ?

i³⁹⁸ = i^4·99+2 = ?

i³⁹⁹ = ?