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This problem involves determining the **Thévenin equivalent impedances** of the two-node network, observed from **Bus 1** (to ground) and **Bus 2** (to ground), based on the given impedance values.

The network parameters are:

- \( Z_1 = j0.1 \, \Omega \)
- \( Z_2 = j0.2 \, \Omega \)

Here's the step-by-step approach:

### 1. **Thévenin Equivalent Impedance Viewed from Bus 1:**

To find the Thévenin equivalent impedance looking from **Bus 1**, we need to "remove" the independent current source at Bus 2 and replace it with an open circuit. The remaining network will consist of impedance \( Z_1 \) (between Bus 1 and Bus 2) and impedance \( Z_2 \) (to ground from Bus 2).

Thus, the impedance seen from Bus 1 to ground will be:

\[
Z_{\text{th,1}} = Z_1 + Z_2
\]

Substituting the values:

\[
Z_{\text{th,1}} = j0.1 \, \Omega + j0.2 \, \Omega = j0.3 \, \Omega
\]

### 2. **Thévenin Equivalent Impedance Viewed from Bus 2:**

To find the Thévenin equivalent impedance viewed from **Bus 2**, we remove the independent current source at Bus 1 and replace it with an open circuit. The remaining impedance seen from Bus 2 to ground is just \( Z_2 \), as the impedance \( Z_1 \) only affects the connection between Bus 1 and Bus 2.

Thus, the impedance seen from Bus 2 to ground will be:

\[
Z_{\text{th,2}} = Z_2 = j0.2 \, \Omega
\]

### Final Answer:
- **Thévenin impedance at Bus 1 (to ground):** \( Z_{\text{th,1}} = j0.3 \, \Omega \)
- **Thévenin impedance at Bus 2 (to ground):** \( Z_{\text{th,2}} = j0.2 \, \Omega \)

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Would you like further details or explanations on this? Here are five related questions to deepen your understanding:

1. How would the Thévenin equivalent impedance change if \( Z_2 \) were purely resistive?
2. What is the significance of the complex impedance in the Thévenin equivalent circuit?
3. How would the analysis change if voltage sources instead of current sources were present in the circuit?
4. Can you find the Thévenin voltage for this circuit?
5. How would you approach this problem using nodal analysis?

**Tip:** When calculating Thévenin impedances, always ensure that independent sources (voltage or current) are replaced by their internal impedances (open circuit for current sources, short circuit for voltage sources).

By manual examination, what are the Thévenin equivalent impedances viewed from Bus 1 (to ground) and Bus 2 (to ground), respectively?

Determine the Thévenin equivalent impedances viewed from Bus 1 (to ground) and Bus 2 (to ground) for a two-node network with impedances Z1 = j0.1Ω and Z2 = j0.2Ω. This solution provides a step-by-step method using Thévenin's theorem and complex impedance calculations.

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