Research suggests that a high level of arousal may be most optimal for the performance of a task when: A. the task is complex. B. the task is simple. C. the rewards are high. D. an audience is present.

Firstly, let us understand that arousal is a physiological and psychological state of being awake, alert and focused, which can affect an individual's performance. Generally, when arousal levels are low, individuals tend to perform poorly; however, as arousal levels increase, so does their performance on tasks.

Now that we understand the relationship between arousal and task performance, let us evaluate each answer choice: A. The task is complex: High levels of arousal might hinder performance on complex tasks due to the potential for increased cognitive load, stress or anxiety. B. The task is simple: High levels of arousal can lead to improved performance on simple tasks, as the person is more alert and focused. C. The rewards are high: This option may cause an increased level of arousal, but it does not directly relate to the task's complexity or how the arousal impacts the performance of the task. D. An audience is present: Having an audience may increase arousal, but again, this option does not directly relate to the complexity of the task or how the arousal impacts the task performance.

Based on the relationship between arousal and task complexity, it is evident that a high level of arousal is most optimal for the performance of a task when the task is simple (option B) since increased alertness and focus can lead to improved performance. Therefore, the correct answer is option "B. the task is simple."