Hello there: hope you can help out with this query even though I'm not a teacher of school student; Just plain curious! What is the result of raising i to the googol power? is there a rule or pattern to raising i by increasing powers of 10?

thanks very much
Paul

Hi Paul,

n in
1 i1 = i
2 i2 = i*i = -1
3 i3 = i*i*i = -i
4 i4 = i*i*i*i = 1
5 i5 = i4*i = i

The pattern repeats i, -1, -i, 1 ... Thus to find ik for k an integer divide k by 4 and let the remainder be r.

If r = 1 then ik = i
If r = 2 then ik = -1
If r = 3 then ik = -i
If r = 0 then ik = 1

For example 2755/4 = 688 with a remainder of 3 so i687 = -i.

Cheers,
Penny
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