Real part

In mathematics, the real part of a complex number $z$ , is the first element of the ordered pair of real numbers representing $z$ , i.e. if $z = (x, y)$ , or equivalently, $z = x + i y$ , then the real part of $z$ is $x$ . It is denoted by $Re z$ or $\Re z$ . The complex function which maps $z$ to the real part of $z$ is not holomorphic.

In terms of the complex conjugate $\bar{z}$ , the real part of $z$ is equal to $z+\bar z\over2$ .

For a complex number in polar form, $z = (r,θ)$ , or equivalently, $z = r (c o s θ + i sinθ)$ , it follows from Euler's formula that $z = r e i θ$ , and hence that the real part of $r e i θ$ is $r cosθ$ .

Real part

See also

See also: Real part, Complex conjugate, Complex function, Complex number, Euler's formula, Holomorphic, Imaginary number, Imaginary part, Mathematics, Ordered pair