19i

19i denotes the complex number formed by multiplying the real number 19 by the imaginary unit i, where i is defined by i^2 = -1. In Cartesian form it is written as 0 + 19i, a purely imaginary number. Geometrically on the complex plane it corresponds to the point (0, 19), located on the positive imaginary axis.

Its magnitude is |19i| = 19, and its argument is pi/2 (90 degrees). In polar form it is 19 cis(pi/2), and in exponential form it is 19 e^{i pi/2}. Its square is (19i)^2 = -361, and its conjugate is -19i.

In arithmetic with real numbers, multiplying 19 by i rotates a real quantity by 90 degrees in the complex plane. It can be added to other complex numbers to form a+bi, or multiplied by i to cycle between real and imaginary components (for instance, i*(19i) = -19). In applied contexts such as electrical engineering and signal processing, imaginary quantities like 19i are used to represent phase relationships in AC signals. While not a standard constant on its own, 19i is a typical example of a purely imaginary complex number that illustrates the basic operations and geometric interpretation of imaginary numbers.