1. The problem statement, all variables and given/known data I'll give an example. Ex: x'=[-1/2 1; -1 -1/2]x. 2. Relevant equations Assume a solution of the form x=$ert for these type of problems. Euler's formula: ebi = cosb + isinb 3. The attempt at a solution |A-rI|=0 ---> r= -1/2 +/- i ---> x= e-t/2 ( C1(cost + isint)(1 i)T + C2(cos(-t) +isin(-t))(1 -i)T ) I understand that I can simplify a little with the fact that sin(-t)=sin(t) and cos(-t)=-cos(t), but I don't understand how to simplify it all the way to C1e-t/2 (cost -sint)T + C2e-t/2(sint cost)T, which is the answer in the book. So, explain.