The imaginary unit shows up in both quantum mechanics and EE as a way to embed i*i = -1 in the equations. Any differential equation that involves it can be writ

The imaginary unit shows up in both quantum mechanics and EE as a way to embed i*i = -1 in the equations. Any differential equation that involves it can be written without it by separating real and imaginary parts into different variables. Furthermore, if you let "one" be represented by the 2x2 identity matrix, the matrix [[0,1],[-1,0]] can act like i in every respect, because that matrix squares to -1 times the identity. In fact, even -i can stand in for i. The "nouns" of math might be real, but whether they are is a metaphysical question; all we observe in science are what you might call the verbs of math. FWIW, the "crossing out the imaginary part" works like this: if the system of equations is linear and doesn't have complex coefficients, every solution has a counterpart solution that is its complex conjugate, and you can add the conjugate (remember, it's linear) to get another, real-valued, solution. You can do that with time-invariant (definite-energy) solutions to the Schrodinger equation as well, because the energy eigenvalue equation doesn't have complex coefficients.