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Imaginary part
In mathematics, the imaginary part of a complex number z, is the second element of the ordered pair of real numbers representing z, i.e. if z = (x,y), or equivalently, z = x + iy, then the imaginary part of z is y. It is denoted by Imz or 
. The complex function which maps z to the imaginary part of z is not holomorphic.
In terms of the complex conjugate 
, the imaginary part of z is equal to 
.
For a complex number in polar form, z = (r,θ), or equivalently, z = r(cosθ + isinθ), it follows from Euler's formula that z = reiθ, and hence that the imaginary part of reiθ is rsinθ.
See also
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details