The Best Common Sense Problem

First let's develop a solution for any given n.If $z^{8n}$ = $z^2$ then $z^{8n-2}$ = 1, Meaning that we can use the (theorem unlisted because of you and you know who you are(Ash Ketchum)).This means that the imaginary part of z is $sin(2K{\pi}/8n-2)$ .Now we can see that the m =4n-1.Now n is simply the sum of all the entries on a 10x10 multiplication grid/100.There is a simple trick we can use to put things in place.The first column is 1(1+2+3+4+5...)and the second is 2(1+2+3+4..) all the way up to 10. we can factor the parentheses out and get (1+2+3+4+5...)(1+2+3+4+5...)=( $11^2$ * $10^2$ )/4 = 3025.Dividing by 100 we have (30.25).(30.25) x 4 -1 =120 our answer.