As far as I know, the most visible way that complex numbers show up "in the real world" is as sine waves. Sine waves of a given frequency can be thought of as complex numbers. Adding together two sine waves corresponds to adding the corresponding complex numbers. Convoluting two sine waves corresponds to multiplying the corresponding complex numbers.
Since every analog signal can be thought of as a sum or integral of sine waves of different frequencies, an analog signal can be represented as a collection of complex numbers, one corresponding to the sinusoid at each frequency. This is what the Fourier transform is. Since convolution of analog signals corresponds to multiplication of their Fourier transforms, now a lot of the stuff we know about multiplication is applicable to convolution as well.
xkcd's Up-Goer Five comic gave technical specifications for the Saturn V rocket using only the 1,000 most common words in the English language.
This seemed to me and Briénne to be a really fun exercise, both for tabooing one's words and for communicating difficult concepts to laypeople. So why not make a game out of it? Pick any tough, important, or interesting argument or idea, and use this text editor to try to describe what you have in mind with extremely common words only.
This is challenging, so if you almost succeed and want to share your results, you can mark words where you had to cheat in *italics*. Bonus points if your explanation is actually useful for gaining a deeper understanding of the idea, or for teaching it, in the spirit of Gödel's Second Incompleteness Theorem Explained in Words of One Syllable.
As an example, here's my attempt to capture the five theses using only top-thousand words:
If you make a really strong computer and it is not very nice, you will not go to space today.
Other ideas to start with: agent, akrasia, Bayes' theorem, Bayesianism, CFAR, cognitive bias, consequentialism, deontology, effective altruism, Everett-style ('Many Worlds') interpretations of quantum mechanics, entropy, evolution, the Great Reductionist Thesis, halting problem, humanism, law of nature, LessWrong, logic, mathematics, the measurement problem, MIRI, Newcomb's problem, Newton's laws of motion, optimization, Pascal's wager, philosophy, preference, proof, rationality, religion, science, Shannon information, signaling, the simulation argument, singularity, sociopathy, the supernatural, superposition, time, timeless decision theory, transfinite numbers, Turing machine, utilitarianism, validity and soundness, virtue ethics, VNM-utility