The electrical engineers use because is already used for current. So you can write a complex number as Here is the real part of written and is the imaginary part of , written This is called the cartesian representation of a complex number.
You can also write complex numbers as a magnitude and an angle - this is called the polar representation of a complex number. That is, where is the magnitude, and is the angle, or argument. Thus you can write and You'll also see this notation, as you've already alluded to:
The transformation from cartesian to polar and back goes like this:
All of these equations come from elementary trigonometry. So, with this information, can you see how they obtained the polar representation from the cartesian one?