Question

The letter i represents the imaginary number √-1. Note that i1=i, i2=-1, i3=-i, i4=1, i5=i,… Use patterns to simplify i2987

Answer 1

do you know the basics of Complex number ?

Answer 2

no

Answer 3

They just rotate, around and around, by 90 degrees each time. Good times!

Answer 4

take the integer remainder when dividing 2987 by 4

Answer 5

since 4 divides 2484 evenly, the remainder is 3

Answer 6

making \(i^{2987}=i^3=-i\)

Answer 7

I like @satellite73 answer much better than what I am about to write, but if modular stuff still seems yucky then you can try this too.

1. i^2987
2. i * i^2986
3. i * (i^2)^1493
4. i * (-1)^[something odd, so remains -1]
5. i * -1 = -i

6. But seriously, the other answer is more elegant in my opinion.

Answer 8

thank you everyone :)