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The phrase "a more complicated example" is correct and usable in written English.
You can use it when introducing a specific instance that illustrates a more complex concept or situation compared to previous examples.
Example: "To better understand the theory, let's look at a more complicated example involving multiple variables."
Alternatives: "a more complex illustration" or "a more intricate case".
Exact(16)
Here's a more complicated example.
We present some simple examples of how the program is used and then present a more complicated example.
All right, so let's think of a more complicated example of having a double bond, and maybe a more interesting example, and this is talking about benzene.
A more complicated example of an implied trust would be the situation in which one party provides money to another for the purchase of property.
The new scheme has been rigorously tested against a simple theoretical solution to Darcy's law as well as a more complicated example solved by numerical software packages with anisotropic flow capabilities.
Herrmann's "Psycho" Suite is a more complicated example, for the film score made use of a previously composed symphonic composition, but most listeners are just waiting for the shower scene anyway.
Similar(44)
In our last example we consider a more complicated model of a phenomenon that is called topographic mapping (van Ooyen, 2003).
Now, we present a little more complicated example of a map, for which we also have.
A slightly more complicated example of a term that has only infinite reduction sequences is Y CKI).
OK, so now let's do a slightly more complicated example.
However, in order to demonstrate some of the difficulties that arise in generalizing from 2-user to -user scenarios, we now discuss a slightly more complicated example than the 2-user 2-subchannel one, namely, the 3-user 2-subchannel scenario depicted in Figure 2.
More suggestions(15)
a more complicated evidence
a more complicated practice
a more complicated experience
a more complicated story
a more complicated case
a more complicated pattern
a more sophisticated example
a more complicated expression
a more complicated picture
a more complicated question
a more egregious example
a more immediate example
a more novelistic example
a more cautionary example
a more familiar example
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com