how do complex numbers help in the study of electromagnetism?

DC electricity can be calculated using only rational, integer numbers.  Edison understood that but he did not understand Math and just could not work with AC like Tesla (super genius) and Westinghouse.

change voltage and current works with Inductors (coils of wire) and Capacitors (parallel plates with an insulator between)

the equations have to be described by calculus equations not just algebra. the algebra formulas are the answers to the Calc EQ.

the Math for the solution requires sin, cos terms written in complex numbers ( a + i b) the (..) is ONE SINGLE UNIQUE NUMBER. It is NOT a ( with a, b, and i) inside.

Complex can be added, subtracted, multiplied and divided.
the catch is that the ''i" turns into a (-1) in the process and gives strange looking answers.

If you want to study AC electricity you must be able to do the
E=I R, calculations using complex instead of real numbers.

that's why EE majors make the big money, If they pass their math courses.