Given:
Pole of the system with initial settling time: -1 + j
Pole of the system with final settling time: -2 + 3j

To determine the settling time of the system when the pole is shifted from -1 + j to -2 + 3j, we need to understand the relationship between settling time and poles in the complex plane.

1. Understanding settling time:
Settling time is a measure of how fast the system reaches and stays within a certain tolerance band around the final value. It is the time taken for the output to reach and stay within a specified percentage (usually 2%) of the final value after a step input.

2. Relationship between poles and settling time:
In general, the settling time is inversely proportional to the real part of the dominant pole(s) of the system. The dominant poles are the ones with the largest real parts.

When the real part of the pole(s) increases, the settling time decreases. Conversely, when the real part of the pole(s) decreases, the settling time increases.

3. Analyzing the given poles:
The initial pole of the system is -1 + j, which has a real part of -1.
The final pole of the system is -2 + 3j, which has a real part of -2.

Since the real part of the pole has increased from -1 to -2, we can expect the settling time to decrease.

4. Determining the new settling time:
The settling time is inversely proportional to the real part of the dominant pole(s). In this case, the dominant pole is -2 + 3j with a real part of -2.

To determine the new settling time, we can use the following relationship:
Settling time(new) = (Settling time(initial)) * (Real part(initial pole) / Real part(final pole))

Substituting the given values:
Settling time(new) = 3 * (-1 / -2) = 3 * (1/2) = 1.5 seconds

Therefore, the settling time when the pole is shifted from -1 + j to -2 + 3j is 1.5 seconds, which corresponds to option B.