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:
“Fiction is not imagination. It is what anticipates imagination by giving it the form of reality. This is quite opposite to our own natural tendency which is to anticipate reality by imagining it, or to flee from it by idealizing it. That is why we shall never inhabit true fiction; we are condemned to the imaginary and nostalgia for the future.”
—Jean Baudrillard (b. 1929)
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)