I did a unit on electronics at uni. Failed the first test, but scraped through on final exam.

In that course, our prof said that the first person to use imaginary numbers in electonics was laughed at! His colleagues said "Imaginary? but circuits are Real ... hahahaha!"

So he used the maths to calculate a circuit which looked normal, but would in fact **short-circuit**. He then put the resistors and capacitors together, showed it to his colleagues, and said "Lo! A short-circuit!" They all laughed again.

So he said, "OK, attach a battery then!"

**Phhzzztt!**

They have used imaginary numbers ever since.