imaginaarne

Imaginaarne is an Estonian adjective meaning "imaginary" or "not real". It is used in everyday language to describe things that exist in the mind or are fictional, as well as in scientific and mathematical contexts to denote nonreal quantities. In mathematics, imaginaarne arv refers to imaginary numbers, which are multiples of the imaginary unit i defined by i^2 = -1. An imaginary number is written as bi, where b is a real number and i is the square root of -1.

A complex number combines a real part and an imaginary part and is written as a + bi, with a and b real. The collection of all complex numbers forms the complex plane, in which real numbers lie on the horizontal axis and imaginary numbers lie on the vertical (imaginary) axis. Key operations include addition and multiplication, as well as taking the complex conjugate a - bi, the modulus sqrt(a^2 + b^2), and the argument arctan(b/a). Imaginary numbers enable the solution of equations with no real solutions and play a central role in fields such as engineering, physics, and signal processing.

Historically, the term imaginary was introduced in the 17th century by Descartes to describe roots of polynomials that are not real; mathematicians later accepted imaginary numbers as a rigorous part of complex analysis. The Estonian term imaginaarne is cognate with German imaginär and English imaginary.

In non-mathematical language, imaginaarne describes things existing only in the imagination, such as imaginary friends or imagined scenarios.