Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...