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

absolute square | complex argument | complex conjugate | complex modulus | complex plane | imaginary number | imaginary part | purely imaginary number | sign