This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Conjugate

 Conjugate[z]or z* gives the complex conjugate of the complex number z.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• can be entered as Esc co Esc, Esc conj Esc, or \[Conjugate].
Use Esc conj Esc to conjugate expressions:
 Out[1]=

Use Esc conj Esc to conjugate expressions:
 Out[1]=
 Scope   (5)
Find complex conjugate of complex exponentials:
Find complex conjugate of explicit algebraic numbers:
The precision of the output does not track the precision of the input:
Infinite arguments give symbolic results:
 Applications   (5)
Define a scalar product for complex-valued lists:
Apply the definition:
Rewrite a complex-valued rational function into one with real denominator:
Recover the original fraction:
Implement a Möbius transformation:
Plot the images of concentric circles:
Write a real-valued function as a function of and :
Holomorphic functions are independent of :
Use Conjugate to describe geometric regions:
Some transformations are performed automatically:
Conjugate is its own inverse:
Simplify expressions containing Conjugate:
Assume real-valued variables:
Assume generic complex-valued variables:
Use Conjugate as an option value in ComplexExpand:
Integrate along a line in the complex plane, symbolically and numerically:
Find Hermitian conjugate of a matrix: