Skip to main content
CareerEd LibreTexts

2: Complex Numbers

  • Page ID
  • [ "article:topic-guide", "license:gnudls", "authorname:tkuphaldt", "license:gnu" ]

    To successfully analyze AC circuits, we need to work with mathematical objects and techniques capable of representing these multi-dimensional quantities. Here is where we need to abandon scalar numbers for something better suited: complex numbers. Just like the example of giving directions from one city to another, AC quantities in a single-frequency circuit have both amplitude (analogy: distance) and phase shift (analogy: direction). A complex number is a single mathematical quantity able to express these two dimensions of amplitude and phase shift at once.