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# Science Fair Project Encyclopedia

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# 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 + iy, then the real part of z is x. It is denoted by Rez 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(cosθ + isinθ), it follows from Euler's formula that z = reiθ, and hence that the real part of reiθ is rcosθ.