BUILT-IN MATHEMATICA SYMBOL

Re

Re[z]
gives the real part of the complex number z.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

Re[expr] is left unevaluated if expr is not a numeric quantity.

Re automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Find the real part of a complex number:

Plot the real part of a complex-valued function:

Use Re to specify regions of the complex plane:

Find the real part of a complex number:

In[1]:=

Out[1]=

Plot the real part of a complex-valued function:

In[1]:=

Out[1]=

Use Re to specify regions of the complex plane:

In[1]:=

Out[1]=

Scope (5)

Mixed-precision complex inputs:

Exact complex inputs:

Algebraic numbers:

Transcendental numbers:

Re threads element-wise over lists:

For some input Re will automatically simplify:

TraditionalForm formatting:

Generalizations & Extensions (1)

Infinite arguments give symbolic results:

Check that the quantity is in the right half-plane:

Applications (3)

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:

Properties & Relations (7)

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:

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:

Possible Issues (1)

Re can stay unevaluated for numeric arguments:

Additional transformation may simplify it:

Neat Examples (1)

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

: