Polar form of complex numbers
The behavior of the current of an electronic circuit or the waves of sound when you play a violin have a sinusoidal behavior. That is something like the following drawing:
when we analyze it, we want to use a simple notation that allows us to comprehend the state of the wave.
If we use the polar form we will have a notation that allow us to know easily the state of the wave (its location).
The polar notation consists in refering to the space with the distance and the angle:
but we can simplify it even more using complex numbers. We can relate the angle of the location with complex numbers.
If we say that the horizontal axis correspond to the real numbers and the vertical axis to the imaginary number we will have an easier way to make operations between distances.
This is why this notation is used in DC circuits, because the operations between the real and imaginary components use exactly the same way as elementary algebra, so the behavior of this kind of circuits can be determined with ease.