Question

simplify: i^(-4n)

Answer 1

i^(-4n) = 1/i^4n ?

Answer 2

You can go further than that

Answer 3

@bedpotato

Answer 4

How so?

Answer 5

What is \(i^4\) equal to?

Answer 6

Is i the imaginary number thing...? I haven't learnt that if it is. If not, then I'm not sure. Sorry.

Answer 7

Yes, i is imaginary

Answer 8

and \(i^4 = 1\)

Answer 9

i know the answer not the working it isn't equal to anything just simplify

Answer 10

So in essence:

\[i^{-4n} = \frac{1}{i^{4n}} = \frac{1}{(1)^n} = \frac{1}{1} = 1\]

Answer 11

yes that's the answer thanks :)

Answer 12

The key to solving this problem, as @Hero mentioned is to recognize that \(\bf i^4=1\).
Once you see that, it is easy to get the answer.

@silvanx

Answer 13

so if you have i^(-4n+1) how is it worked out?

Answer 14

You mean

\[i^{-4n + 1} = i^{-4n}\times i = \frac{i}{i^{4n}} = \frac{i}{4} = \frac{\sqrt{-1}}{\sqrt{16}}= \sqrt{\frac{-1}{16}} = \sqrt{-\frac{1}{16}}\]

Answer 15

Hang on...I think I may have gotten a bit carried away

Answer 16

it's supposed to be i/1

Answer 17

It simplifies to \(i\)

Answer 18

thanks a lot :)

Answer 19

You can remember i^2=(-1),i is assigned this imaginative value!!
Hence i^4=1....