Your regexp would match both "complex.12" and "complex.120", because though it is only looking for "complex." followed by two digits, it doesn't exclude anything that exceeds the minimum criteria.

Perhaps you meant to say:

m/^complex\.\d{2}$/
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...or...

m/\bcomplex\.\d{2}(?!\d)/
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The first example requires that the string contain nothing at all besides "complex.nn" (where nn is two digits). The second example allows the string to contain additional stuff, but requires that the "complex.nn" tag be clearly bounded by a word boundry on the left, and a digit-boundry on the right.