The imaginary part ![I[z]](/images/equations/ImaginaryPart/Inline1.svg)
of a complex number 
is the real number multiplying
i, so ![I[x+iy]=y](/images/equations/ImaginaryPart/Inline3.svg)
. In terms of 
itself,
![I[z]=(z-z^_)/(2i),](/images/equations/ImaginaryPart/NumberedEquation1.svg) |
where 
is the complex conjugate of 
. The imaginary part is implemented in the Wolfram
Language as Im[z].
Imaginary Part
See also
Absolute Square, Complex Argument, Complex Conjugate, Complex Modulus, Complex Plane, Imaginary Number, Purely Imaginary Number, Real Part, SignRelated Wolfram sites
http://functions.wolfram.com/ComplexComponents/Im/Explore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 16, 1972.Krantz, S. G. Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 2, 1999.Referenced on Wolfram|Alpha
Imaginary PartCite this as:
Weisstein, Eric W. "Imaginary Part." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ImaginaryPart.html