1. Find the real part of 1 + ((1+i)/√2) + ((1+i)/√2)2 +...+ ((1+i)/√2)2008

One possible solution: let z=(1+i)/√2= cos(pi/4) + i sin(pi/4). Then


2. Compute (1+i)2013/(1-i)2011

3. There are six complex numbers satisfying z6+1=0. Find the sum of all of them.