Compute \(1+i+i^2+i^3+i^4+\cdots+i^{2009}\).
\(2010/4=502R2 \\ 1+i+i^2+i^3+i^4+\cdots+i^{2009} \\=1+i+-1+-i\\ +1+i+-1+-i+.......\\~\\ =0+1+i\\ =1+i \)
