An imaginary number is a number whose square is less than or equal to zero. For example, is an imaginary number and its square is . An imaginary number can be written as a real number multiplied by the imaginary unit, which is defined by its property .
An imaginary number can be added to a real number to form a complex number of the form, where and are called, respectively, the real part and the imaginary part of the complex number. Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless, but today they have a variety of essential, concrete applications in science and engineering.
Read more about Imaginary Number: History, Geometric Interpretation, Applications of Imaginary Numbers, Multiplication of Square Roots
Famous quotes containing the words imaginary and/or number:
“Avarice, the spur of industry, is so obstinate a passion, and works its way through so many real dangers and difficulties, that it is not likely to be scared by an imaginary danger, which is so small that it scarcely admits of calculation.”
—David Hume (1711–1776)
“It is always possible to bind together a considerable number of people in love, so long as there are other people left over to receive the manifestations of their aggression.”
—Sigmund Freud (1856–1939)