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Complex Conjugate

Complex Conjugate

The complex conjugate of a + bi  is a – bi, and similarly the complex conjugate of a – bi  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, Math equation showing the complex conjugate notation: 3 + 7i = 3 − 7i, with a horizontal bar over the left side..

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

Expression Lowercase italic letter z, representing a complex number variable used in complex conjugate notation. Complex Conjugate z-bar (z with a horizontal overline), representing the complex conjugate notation of variable z
5 – 2i
4i + 1
–5i
12
Math expression showing 2 + √6, an example of a complex conjugate expression.
5 + 2i
–4i + 1
5i
12
Math expression showing 2 + √6, an example of a complex conjugate expression.

 

See also

Complex number formulas