This is not a normal problem help topic. The difficulty I've encountered is in understanding an alternative solution. 1. The problem statement, all variables and given/known data In a real conductor, electrons (with mass m), conducted by external electric fields, constantly collide with defects and impurities within the conductor. The average effect of those collisions is similar to a viscosity force ƒ= -mv/τ (ƒ and v have vector hats), where τ is a constant parameter, named collision time. 1. Write the second law of dynamics that helps finding the speed of an electron. Ignore the interactions between electrons. 2. Consider that E(t) = E0 sinωt (E and E0 have vector hats), find the expression for the speed of an electron. Note: it's convenient to use the complex form E(t) = E0 eiωt. You can use eiθ = cosθ +i sinθ. ....(there are other tasks, but they are rather easy) 2. Relevant equations ma +mv/τ = qE0 sinωt (a, v, E do not have vector hats) ma= -mv/τ - qE0 eiωt (a, v, E are vectors) 3. The attempt at a solution I can solve the first differential equation (that is the equation I have derived) the classical way (find homogeneous and particular solutions). Tough, in the key, they write the equation in the second form and then they get the next equation: iωmv= -mv/τ - qE0 (v, E are vectors) What is the explanation for their equation. I just can't get it.