Imaginary Number
Although Descartes originally used the term "imaginary number" to refer to what is today known as a complex number, in
standard usage today, "imaginary number" means a complex
number 
that has zero real
part (i.e., such that ![R[z]=0](/National_Library/20160521004321im_/http://mathworld.wolfram.com/images/equations/ImaginaryNumber/Inline2.gif)
). For clarity,
such numbers are perhaps best referred to as purely
imaginary numbers.
A (purely) imaginary number can be written as a real number multiplied by the "imaginary unit" i (equal to the square root 
), i.e., in the form 
.
In the novel The Da Vinci Code, the character Robert Langdon jokes that character Sophie Neveu
"believes in the imaginary number 
because it helps
her break code" (Brown 2003, p. 351). In Isaac Asimov's short story "The
Imaginary" (1942), eccentric psychologist Tan Porus explains the behavior of
a mysterious species of squid by using imaginary numbers in the equations which describe
its psychology. The anthology Imaginary
Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings
(Frucht 2000) includes many other works involving imaginary numbers.
Contact the MathWorld Team
imaginary number
