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:
“Girls are apt to imagine noble and enchanting and totally imaginary figures in their own minds; they have fanciful extravagant ideas about men, and sentiment, and life; and then they innocently endow somebody or other with all the perfections for their daydreams, and put their trust in him.”
—Honoré De Balzac (1799–1850)
“At thirty years a woman asks her lover to give her back the esteem she has forfeited for his sake; she lives only for him, her thoughts are full of his future, he must have a great career, she bids him make it glorious; she can obey, entreat, command, humble herself, or rise in pride; times without number she brings comfort when a young girl can only make moan.”
—Honoré De Balzac (1799–1850)