Question about simplification

I have been given

1/2pi*[ (2pi*(-1)^n)/-i*n)]= (i*(-1)^n)/n

However I just get the 2pi cancelling each other out and getting

((-1)^n)/(i*n)

This is surely just an error in the sheet right or am I missing something?

What're you trying to find??

Are you trying to rearrange the first on into the second?

Do you have

$\dfrac{1}{2 \pi}\dfrac{2 \pi (-1)^n}{(-i)^n}$

or

$\dfrac{1}{2 \pi}\dfrac{2 \pi (-1)^n}{-(i)^n}$

the bottom line is i*n, not to the power.
Basically its the first question from this page
http://math.ucsd.edu/~lni/math140/HW140B_8_solutions.pdf

I don't understand how they have gotten from the 4th line to the 5th

So you have

$\dfrac{(-1)^n}{-in}$

I assume that they multiplied numerator and denominator by i

though I have not looked at your link

There answer is

(i(-1)^n)/n

If i multiplied the numerator and denominator by i, I get

(i((-1)^n))/((-i^2)n)

I assume that you know what $i^2$ is

So that you know what -$i^2$ is

Well I just found out it equals -1 and it makes complete sense now. I didn't think you could just square it like another number before for some reason. Certainly makes my life easier, anyway thanks for your help!

Did you not know that $i = \sqrt{-1}$

Are you self teaching?

I do, I've known that for ages! Its just for some reason I didn't think you could just square it like another number and then it would just equal minus 1.

And well i rarely go to lectures... so in a way lol

I definitely should have cottoned on earlier, but when i've looked at something for so long and i'm sure they've just made a typo, i can get stuck on ridiculousy easy things.

Fair enough

We usually rationalise the denominator so anything with i in the denominator will need to be * by something