L worked at the night, and he returned home at the morning. He wanted to sleep. S was going to work, and said something to L. L said he worked at night and wanted to sleep. S still insist L to drive and to send S to work. Then L complained
Didn't I tell I'd be working nights?
Since "working at night" and "L telling S about this" all happened in the past, why here use "would be doing"?
It is in the past tense. This is a "future in the past" construction. The question is rhetorical. Leonard isn't looking for an answer, but he phrases his statement as a question. Changing it back to a statement gives:
I told you I would be working nights.
So in the past Leonard said "I will be working nights". In the past Leonard used a future tense. When he reports this the tense of "will" is changed to the past tense. The past tense of "will" is "would".
This construction is quite rare, it is most likely to appear in reported speech, thoughts or emotions
I knew it would be fun.
Leonard could have used a "going to" for the future with little or no change in meaning.
Didn't I tell you I was going to be working nights?
It's not "would be doing", it's "would be sth".
Working nights is a idiom means the shift of working at night.
"Would" indicates that all the "L telling S about working nights thing" happened in the past, not this morning, it might be yesterday.
