Academy of Sciences of Heroesland

Remember the imaginary exponential: it can always be expressed through a combination of sines and cosines – which are real numbers.

I didn't quite understand what you were talking about. Sometimes, to simplify intermediate calculations, you can assume a physical quantity is complex and, after performing the necessary transformations, confidently switch to real numbers, realizing that the imaginary part itself doesn't carry any physical meaning. But how do you get a real number from an imaginary number?