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Real Part

RePart

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself,

R[z]=1/2(z+z^_),

where z^_ is the complex conjugate of z. 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/

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

Real Part

Cite this as:

Weisstein, Eric W. "Real Part." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RealPart.html

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