Real Part

In mathematics, the real part of a complex number z, is the first element of the ordered pair of real numbers representing z, i.e. if z = (x, y) , or equivalently, z = x+iy, then the real part of z is x. It is denotated by \mbox{Re}z or \Re z. The complex function which maps z to the real part of z is not holomorphic. In terms of the complex conjugate\bar{z}, the real part of z is equal to z+\bar z\over2. For a complex number in polar form, z = (r, \theta ), or equivalently, z = r(cos \theta + i \sin \theta) , it follows from Euler's formula that z = re^{i\theta}, and hence that the real part of re^{i\theta} is r\cos\theta.

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