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, .

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