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Complex Conjugate

The complex conjugate of a + bi  is abi, and similarly the complex conjugate of abi  is a + bi. This consists of changing the sign of the imaginary part of a complex number. The real part is left unchanged.

Complex conjugates are indicated using a horizontal line over the number or variable. For example, .

Note: Complex conjugates are similar to, but not the same as, conjugates.

Expression Complex Conjugate
5 – 2i
4i + 1
–5i
12
5 + 2i
–4i + 1
5i
12

 

See also

Complex number formulas

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes