▲In [[mathematics]], the '''imaginary part''' of a [[complex number]] <math> z</math>, is the second element of the ordered pair of [[real number]]s representing <math>z,</math> i.e. if <math> z = (x, y) </math>, or equivalently, <math>z = x+iy</math>, then the imaginary part of <math>z</math> is <math>y</math>. It is denoted by <math>\mbox{Im}z</math> or <math>\Im z</math>. The [[complex function]] which maps <math> z</math> to the imaginary part of <math>z</math> is not [[holomorphic]].
In termstermini of thedi [[complexcomplesso conjugateconiugato]] <math>\bar{z}</math>, thela imaginaryparte partimmaginaria ofdi ''z'' isè equaluguale toa <math>\frac{z-\bar{z}}{2i}</math>.
ForPer aun complexnumero numbercomplesso in [[polarcordinate coordinatespolari|polarforma formpolare]], <math> z = (r, \theta )</math>, oro equivalentlyequivalentemente, <math> z = r(cos \theta + i \sin \theta) </math>, itsegue follows fromdalla [[Euler's formula di Eulero]] thatche <math>z = re^{i\theta}</math>, ande hencequindi thatche thela imaginaryparte partimmaginaria ofdi <math>re^{i\theta} </math> issia <math>r\sin\theta</math>.
