Find the real part of a complex number:

Find the real part of a complex number expressed in polar form:

Plot over a subset of the complex plane:

Use Re to specify regions of the complex plane:

Flow around a cylinder as the real part of a complex‐valued function:

Construct a bivariate real harmonic function from a complex function:

The real part satisfies Laplace's equation:

Reconstruct an analytic function from its real part :

Example reconstruction:

Check the result:

Use Simplify and FullSimplify to simplify expressions containing Re:

Prove that the disk is in the right half-plane:

ComplexExpand assumes variables to be real:

Here z is not assumed real, and the result should be in terms of Re and Im:

FunctionExpand does not assume variables to be real:

ReImPlot plots the real and imaginary parts of a function:

Use Re to describe regions in the complex plane:

Reduce can solve equations and inequalities involving Re:

With FindInstance you can get sample points of regions:

Use Re in Assumptions:

Integrate often generates conditions in terms of Re:

Re can stay unevaluated for numeric arguments:

Additional transformation may simplify it:

Re is a function of a complex variable and is therefore not differentiable:

As a complex function, it is not possible to write Re[z] without involving Conjugate[z]:

In particular, the limit that defines the derivative is direction dependent and therefore does not exist:

Use ComplexExpand to get differentiable expressions for real-valued variables:

Use Re to plot a 3D projection of the Riemann surface of :