A complex subject includes both a noun or noun phrase and any other words or phrases used to describe the subject. Take this sentence, for example:
The ascent of Mt Everest amazed the world.
Usual procedure - identify the verb to help us find the subject of the sentence. The verb is ‘amazed’. When we look for who or what is doing the ‘amazing’, we find the subject - ‘the ascent of Mt Everest’. This is known as a complex subject.
Now, any complex subject always has a central noun - the noun around which the rest of the subject is organised. In this case, it’s the noun ‘ascent’. ‘Of Mt Everest’ is a modifier which tells us extra information about the noun ‘ascent’.