1. An 820-Ω resistor is connected in parallel with a 1000-pF capacitor. The impedance of the parallel combination is 410 - j410 Ω. Find the frequency.
2. Two impedances Z1 = 300 - j50 Ω and Z2 = 450 + j100 Ω are connected in parallel. Find the equivalent impedance of the pair.
3. A 100-mH inductor and a 100-Ω resistor are connected in parallel. The circuit is excited by a voltage source with vS(t) = 10 cos (1 kt - 45°) V. What is the steady-state current iS(t) flowing from the source?