Definition of the Complex Conjugate

The complex conjugate is found by taking the sign of the imaginary portion of a complex number and changing it to the opposite sign.

If there is a complex number,

$ a + bi $

where $ a $ and $ b $ are arbitrary constants, then the complex conjugate is

$ a - bi $.

Vice versa, if there is a complex number

$ a - bi $

then the complex conjugate is

$ a + bi $.