Consider this geometric sequence: i0, i1, i2, i3, i4, i5 , …, i15.
You know that i0 = 1, i1 = i, and i2 = −1. Calculate the result for each term up to i15, and describe the pattern.
i0 = 1 Can you see the pattern?
i1 = i
i2 = −1
i3 = (i)(i2) = −i
i4 = (i2)(i2) = 1
i5 = (i2)(i2)(i) = i
The pattern repeats 1, i, −1, and −i
Use the pattern you found in part (a) to calculate i16, i25, i39, and i100.
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.
i16 = 1
i25 = i
i39 = −i
i100 = 1
What is i4n , where n is a positive whole number?
4n is a multiple of 4.
Based on your answer to part (c), simplify i4n+1, i4n+2, and i4n+3.
Refer to (a), (b), and (c).
Calculate i396, i397, i398, and i399.
i396 = i4·99 = 1
i397 = i4·99+1 = ?
i398 = i4·99+2 = ?
i399 = ?