Question: Cambridge Dictionary gives this definition about "complain"

> 
> to say that something is wrong or not satisfactory
> 
> 
> 

and this definition about "complaint"

> 
> a statement that something is wrong or not satisfactory
> 
> 
> 

I guess both of them means the same thing. However, [Google Ngram](https://books.google.com/ngrams/graph?content=to%20complain%20about%2C%20make%20a%20complaint%20about%20&case_insensitive=on&year_start=1800&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cto%20complain%20about%3B%2Cc0%3B.t1%3B%2Cmake%20a%20complaint%20about%3B%2Cc0#t1%3B%2Cto%20complain%20about%3B%2Cc0%3B.t1%3B%2Cmake%20a%20complaint%20about%3B%2Cc0) shows that the former is much more commonly used that the latter

[![enter image description here](https://i.stack.imgur.com/IyIrh.png)](https://i.stack.imgur.com/IyIrh.png)

Are those two expressions interchangeable?

Answer: 
It all depends on the way you define what *sentence* means in your context.

If you mean the string between two periods, then yes, a sentence can have an arbitrary number of conjugated verbs, and hence *is* and *are* in one sentence are allowed. For example:

> 
> The weather is fine and all people are happy.
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> 
> 

If you consider a sentence to be the part containing subject and conjugated verb (or an infinitive sentence), then it is not possible. Then, the example above must be considered as two sentences that are contactenated.

The example in your question is really a sentence and its subclause - so it is one sentence in the first sense but two sentences in the latter sense. For better readability, there should be a *that* in between:

> 
> The conclusion is that both are harmful.
> 
> 
>
No reason they can't be used in the same sentence, but for the sentence you provided it's incorrect.

The context of the question is "can you use both or only one", so "both" is *a solution* and therefore:

"The conclusion is [the use of] both is harmful."

In the original sentence, "The conclusion is both are harmful.", this is implying that *both* words "is" and "are" are independently harmful, and they are not both harmful.