Explanation:
The correct answer is "have lost". In English, the present perfect tense is used to describe an action that started in the past and has a connection to the present. In this case, the action of losing the key started in the past and has an impact on the present situation of not being able to find it. Let's break down the explanation further:

Present Perfect Tense
The present perfect tense is formed using the auxiliary verb "have" or "has" followed by the past participle of the main verb. In this case, the verb "lose" is in the past participle form "lost" after the auxiliary verb "have".

Connection to the Present
By using the present perfect tense, we indicate that the action of losing the key has a connection to the present moment. It suggests that the key is still lost and has not been found yet.

Use of the Simple Past Tense
If we were to use the simple past tense ("lost") in this sentence, it would imply that the action of losing the key occurred at a specific moment in the past, but it would not have a direct connection to the present. It would simply state that the key was lost in the past without any indication of the current situation.

Additional Context
In the given sentence, the speaker states "I have lost my key." The use of "have lost" suggests that the action of losing the key happened in the past, and it has an impact on the present situation of not being able to find it. The sentence indicates that the speaker is currently unable to locate their key due to the action of losing it in the past.

Conclusion
Using the present perfect tense "have lost" accurately conveys the ongoing nature of the action of losing the key and its connection to the present situation of not being able to find it. The correct answer emphasizes the relationship between the past action and the present state.