I'm currently working through Cogdell's Foundations of Electrical Circuits and came across problem 4.39 d) as shown below:
Earlier in the question I found the frequency-to-be-used as 43.3x10^3 rad/s. Now, in order to make the circuit appear purely resistive the reactive part needs to sum to 0. In part c) of the question the capacitance was being added in series, so I simply used wL-(1/wC)=0. For d) however, the capacitance is to be in parallel with the inductor, leading to the (seemingly) unsolvable equation:
The book says the answer is C=0.1uF, and that it should lead to a real impedance of 400ohms. The only approach to this question I haven't taken is using the formula for the impedance angle for an R(L||C) circuit, but I'm not actually sure what that formula is. Any insight or hints are appreciated! Thanks.