Imaginary numbers can seem confusing at first, but they play a powerful role in mathematics and real-world applications. This ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...