Hello! As someone who tutors middle/high schoolers, I'm frequently asked about imaginary numbers, and students frequently tell me imaginary numbers are "made up" to make up more problems that we don't need to solve. Obviously, as a college student, I'm aware that imaginary numbers are crucial to real-life applications, but I'm having trouble saying anything else other than "imaginary numbers are important in electromagnetism which is crucial for electronics and most of modern inventions regarding electronics."
Is there something I could tell them that convinces them otherwise?