Imaginary Number (Noun)
Meaning
(mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1.
Classification
Nouns denoting quantities and units of measure.
Examples
- The complex plane is a geometric representation of the algebra of complex numbers, which are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.
- In the 18th century, mathematicians such as Leonhard Euler and Caspar Wessel began to use the imaginary number i to extend the real numbers to the complex numbers.
- Imaginary numbers are used in many fields, including electrical engineering, signal processing, and control theory, to represent quantities that have both magnitude and direction.
- Complex analysis is the study of functions of a complex variable, which takes values in the complex plane, where each point is identified with an imaginary number of the form a + bi.
- The square root of -1, denoted by i, is the fundamental imaginary number that defines the complex numbers, and it satisfies the equation i^2 = -1.