Taking a leap of faith into imaginary numbers opens new doors in the real world through complex analysis

Imaginary numbers push the boundaries of calculus and other branches of math. Hill Street Studios/DigitalVision via Getty Images

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be hard to wrap your head around. If you open your mind to this way of thinking, however, a whole new world becomes possible.

I’m a mathematician who studies analysis: an area of math that deals with complex numbers. Unlike the more familiar real numbers – positive and negative integers, fractions, square roots, cube roots and even numbers such as pi – complex numbers have an imaginary component. This means they are made of both real numbers and the imaginary number i: the square root of negative 1.