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# Re

 Re[z]gives the real part of the complex number z.
• 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.
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:
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Plot the real part of a complex-valued function:
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Use Re to specify regions of the complex plane:
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 Scope   (5)
Mixed-precision complex inputs:
Exact complex inputs:
Algebraic numbers:
Transcendental numbers:
For some input Re will automatically simplify:
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:
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:
Re can stay unevaluated for numeric arguments: