If I had a dollar for every explanation of complex numbers that is basically just "A complex number is a real number plus an imaginary component, where i = sqrt(1)" I would almost have enough money to go back to uni and study math. It's far enough through the curriculum that most people get through the class by symbolic pattern matching and algorithmic question-answering rather than actual understanding (I studied EE), and I am pretty certain that even most (note, most) professors only really understand them as a quirky trick of our mathematical system. Ask them to explain it in English, not just as a mathematical definition, they all seem to come unstuck.<p>This old but very good lecture series really helped me - I can at least accept that complex numbers are not some ficticious hack now - but I confess I still dont have an intuitive grasp of complex numbers.<p><a href="https://youtu.be/BOx8LRyr8mU" rel="nofollow">https://youtu.be/BOx8LRyr8mU</a>