The real part of a complex number is the real number not multiplying i, so . In terms of itself,
where is the complex conjugate of . The real part is implemented in the Wolfram Language as Re[z].
A nonzero complex number with zero real part is called an imaginary number or sometimes, for emphasis, a purely imaginary number.
See also
Absolute Square, Complex Argument, Complex Conjugate, Complex Modulus, Complex Plane, Imaginary Number, Imaginary Part, Purely Imaginary Number, Sign
Related Wolfram sites
http://functions.wolfram.com/ComplexComponents/Re/
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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
Cite this as:
Weisstein, Eric W. "Real Part." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RealPart.html