SOLUTION: How would you solve the problem i^7+i^2+i^12+i^9 over (1-i)^2?

Question 134532: How would you solve the problem i^7+i^2+i^12+i^9 over (1-i)^2?
Found 2 solutions by Earlsdon, josmiceli:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First, it would be helpful to have a table of values for . You can do this quite easily:

because =

Do you see the pattern?
Simplify:
=

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

Note that

So, the sequence is
i, -1, -i, 1, i, -1, -i, 1
If the exponent is 1,5,9,13. . . every other odd #, then

If the exponent is 3,7,11,15 . . .every other odd #, then

If the exponent is 2,6,10,14 . . .every other even #, then

If the exponent is 4,8,12,16 . . .every other even #, then

Unless I goofed, the answer is

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