HI Leibniz, I wanted to share a quick insight: "Complicated" describes something with many parts that's tough but doable, like putting together furniture. "Complex" means many interconnected parts that act unpredictably, like an ecosystem or the human brain. I hope this helps, all the Best, Harry

"Complications" are difficult to resolve, but might be structurally quite simple. For example, the task of finding two people in the New York City telephone directory such that one person's name is the other person's name spelled backwards would be a complicated task but little intelligence is needed to do it. It is not complex. A "complex" situation requires intelligence to be understood.

‘Complicated’ is a more common word, used in everyday American English to describe things like relationships and situations that aren’t simply described and could even contain uncertainty. A: Who was that woman I saw you with? B: It’s complicated. (Not ‘complex’) ‘Complex’ sounds more formal and scientific. All languages have a complex grammar. You can usually replace ‘complex’ with ‘complicated’ but it’s not as precise-sounding in an academic context.

The meanings do overlap. A watch is "complicated." A car engine is "complicated." A musical piece where all the instruments all play different melodies that fit together into harmonious whole is "complicated." Human emotions are "complex." The growth of a tree is "complex." The motion of a sailing ship, driven by wind and waves, is "complex." "Complicated" tends to be used when there are visible, separate pieces. It suggests machinery, literally or figuratively. Also, "complicated" is an everyday word that can be used in writing or conversation. "Complex" is slightly more formal. "Complicated" might be a safer choice if you are not sure which to use.

If you can break it down into a series of steps, even if it's a long series, it's probably complicated. If the whole is more than the sum of its parts, and the interactions between parts are what make it hard to understand, it's complex. As for frequency, it depends on the context.