i can't figure this out?

Question

i^-87
show your work

Answer 1

i^-87
=1/i^87
=1/[(i^4)^21*i^3]
=1/(1^21*i^3)
=1/(1*i^3)
=1/(1*-i)
=1/(-i)
=-i

Answer 2

i = j = imaginary number, right??

In which case i to the power of 87 would be -i

since i to the power of 88 would be = 1.
i to the power or 86 = - 1
& i to the power of 85 = i

It's more or less an exercise in division. 88 is divisable by 4. and thus any number which is divisible by 4, would have the save value as i ^ 4 = 1. 87 is the one below i ^ 4, which is i ^ 3 = - i

Answer 3

I am assuming i is complex number,

where i^2 = -1

therefore i^4 = i^2 x i^2 = -1 x -1 = 1

So,

i^-87 = 1/i^87 = 1/(i^84 x i^3)

= 1/i^3

= -i^-1

Answer 4

1/i^87, 87/4=21 3/4 so negative square root one is answer.

Pattern for imaginaries...

i=square root of -1, i^2=-1, i^3= negative square root of -1, i^4=1