Real Part

The real part $\Re$ of a Complex Number $z=x+iy$ is the Real Number not multiplying i, so $\Re[x+iy]=x$. In terms of $z$ itself,

$$\Re[z]={\textstyle{1\over 2}}(z+z^*),$$

where $z^*$ is the Complex Conjugate of $z$.

See also Absolute Square, Complex Conjugate, Imaginary Part

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 16, 1972.