Problem 2: Look at the AC circuit we discussed in Lecture on 20220412, which had an AC generator V, w, a resistor R, a capacitor C', and an inductor L, all in parallel. The AC generator produces a timedependent voltage V(t) = V0 cos(wt) = Re{I/b exp(wt)} , (2) and it led to sinusoidally varying currents 136), 10(t),IL(t) in each of the three parallel legs, some of which had cos(w t) and some of which had sin(w t) dependence. State a clear argument that each of these currents can be ex pressed in the form I(t)=Re{% exp(iwt)} , (3) if we we associate an impedance to each of the circuit elements as follows: ZR = R (4) 1 Z0 2 tau 0 (5) Z L = iw L . (6) At some point you might need to use the facts 2'2 = 1 and 1/2' = 2'. Or not