2yi

2yi is a symbolic expression used in mathematics to denote twice the real parameter y multiplied by i, where i is the imaginary unit defined by i^2 = -1. If y is real, 2yi is a purely imaginary number with no real part.

In the complex plane, it corresponds to the point (0, 2y) on the imaginary axis, with magnitude |2y| and argument π/2 for y>0 and -π/2 for y<0; when y=0 the value is 0 and its argument is undefined.

As a compact notation, 2yi is often encountered in algebraic manipulations, polynomial factorization, and when expressing solutions with imaginary components. For example, with y=3, 2yi equals 6i; with y=-1, it equals -2i.

In many contexts the symbol y is treated as a real parameter, though the same expression can be extended to complex y, in which case 2yi depends on the complex product 2*y*i.

See also complex number, imaginary unit, imaginary axis.