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:
“Understanding replaces imaginary fears with real ones.”
—Mason Cooley (b. 1927)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)