Figure 4. A snapshot, in time, of two complex numbers whose exponents, and thus their phase angles, change with time. The notion of negative frequency is often troubling to engineers who've spent so ...

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 ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...