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:
“We do not content ourselves with the life we have in ourselves and in our being; we desire to live an imaginary life in the mind of others, and for this purpose we endeavor to shine. We labor unceasingly to adorn and preserve this imaginary existence and neglect the real.”
—Blaise Pascal (16231662)
“There is not to be found, in all history, any miracle attested by a sufficient number of men, of such unquestioned good sense, education, and learning, as to secure us against all delusion in themselves ... beyond all suspicion of any design to deceive others ... and at the same time attesting facts, performed in such a public manner, and in so celebrated a part of the world, as to render the detection unavoidable.”
—David Hume (17111776)