Question

This week we study complex numbers which include an "imaginary" part. This is an unfortunate name,  because imaginary numbers can be proven to exist and they are very useful for describing certain physical phenomena. Search for one interesting fact about imaginary numbers. This can be their history, application, etc. Be sure to read through your classmates' postings first, duplicate facts will not count.

a. What is your fact?

b. In your secondary responses to your classmates' facts, endeavor to expand our knowledge or understanding of how they affect the world as we know it.

Answer 1

The History of Imaginary Numbers

Heron of Alexandria (CE 100) is thought to be the first person proposing that the square root of a number (√63) could be a solution to a problem.

Niccolò Fontana (Tartaglia), Gerolamo Cardano and Lodovico Ferrari developed a formula in the early 16th century for finding the roots of cubic equations. Their work was published in the 1545 book Ars Magna. The formula included the roots of -1, which they realized didn’t exist. At the time, the numbers were called these non-existent numbers “numeri ficti.” Although they appeared in the equations, they ended up canceling out, so there was no need to figure out what they actually were. In 1572, Rafael Bombelli explained what the numeri ficti were and what they could be used for.

Rene Descartes came up with the phrase “imaginary numbers,” in the 17th century; mentioned in La Geometrie, it was meant to be a derogatory term. In the 18th century, the Swiss mathematician Leonhard Euler came up with the notation i as being equal to the square root of -1. Carl Friedrich Gausspopularized the use of imaginary numbers in the 19th century.

b)Imaginary numbers are mainly used in mathematical modeling. They can affect values in models where the state of a model at a particular moment in time is affected by the state of a model at an earlier time. You’re most likely to use imaginary numbers in fields like quantum mechanics and engineering where differential equations are used (differential equations are part of calculus). For example, they can be used to monitor the phase and amplitude of an audio signal or electrical currents. You’ll also come across these numbers in computer science, where some programming languages (like C#) use imaginary numbers in their routines. Imaginary numbers are very rarely used in statistics; you’ll come across them in advanced topics like Fourier Analysis.