Complexity is about the number of interoperating parts. A math problem like 75533787543269^634678 may be difficult to do with pen and paper, but it's not complicated, whereas, take the result of 5^2, divide by the number of e's in these song lyrics, take that number of steps due North, and incline your head 60° while facing 3 o'clock - is a complicated set of directions even if none of the calculations are as difficult as the simpler one above.
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