The problem at hand is to rewrite the complex fraction (8 - i) divided by (3 - 2i) in the standard form for a complex number, which is "a + bi", where "a" and "b" are real numbers, and "i" is the imaginary unit. The task is to find the real part of the complex number after performing the division, which is the value of "a".

To solve this problem, you can follow the given steps:

1. 1. Multiply both the numerator and the denominator by the conjugate of the denominator, which is (3 + 2i).
2. 2. Perform the multiplication using the distributive property (FOIL method) and simplify the results.
3. 3. The denominator will become a real number since the imaginary parts will cancel out.
4. 4. Divide the numerator by the denominator, and you'll get the real part "a".

For example, when the numerator, (8 - i), is multiplied by the conjugate of the denominator, (3 + 2i), and the denominator, (3 - 2i), is multiplied by its conjugate, the simplified result is (26 + 13i) / 13 = 2 + i.

Therefore, the real part "a" of the complex number is 2. Hence, the final answer is A) 2.

By following these steps, the problem has been successfully solved, and the real part of the complex number has been determined.

This image illustrates two different approaches to machine learning architectures for handling multiple tasks.

(a) Individual Task-Specific Adaptation: This design describes a multi-task learning framework where each task has its own dedicated layers on top of a shared backbone. The shared backbone layers are common to all tasks, which helps in learning common features but does not adapt to any task specifically. Then, for each task (Task 1, Task 2, Task 3), there are additional layers specific to that task built on top of the shared backbone. These task-specific layers are meant to fine-tune the network for that particular task.

The formula Latency(T_total) ∝ N_tasks * Latency(T_single-task) indicates that the total latency (or computational time) for processing all tasks is proportional to the number of tasks multiplied by the latency of processing a single task. This suggests that the latency grows linearly with the number of tasks, which could become a bottleneck as the number of tasks increases.

(b) Shared Multi-Task Adaptation (Ours): The second design, labelled as "ours", suggests an improvement over the first. In this framework, the multi-task learning architecture again has shared backbone layers, but rather than individual task-specific layers, there is a shared multi-task adaptation mechanism. This adaptation mechanism serves all tasks and is engineered to be efficient. As a result, the architecture is designed to process multiple tasks without a linear increase in total latency.

The formula Latency(T_total) ∝ Latency(T_single-task) indicates that in this improved model, the total latency for all tasks is proportional to the latency of processing a single task, which implies that adding more tasks does not necessarily increase the total computational time by an amount directly proportional to the number of new tasks. This hints at a more efficient use of computational resources, leading to potential savings in time and possibly power consumption.

Both images show an evolution of multi-task learning architectures with the latter one aiming to be more efficient by sharing not only the backbone layers but also the task adaptation mechanism. This shared multi-task adaptation could be achieved through techniques like attention mechanisms, conditional computation, or other forms of task-dependent network modulation that don't significantly add to the computational burden.