Complex conjugate

Complex Conjugate

To put it simply, to take the complex conjugate of something is just to replace $j$ with $-j$. A star ($*$) is used to show that the complex conjugate is being taken.

Example 1: $(a+jb)^{*}=(a-jb)$

Notice, it is just the sign of $j$ that changed.

Example 2: $(e^{j\omega })^{*}=e^{-j\omega }$

Example 3: $(cos\omega -jsin\omega )^{*}=(cos\omega +jsin\omega )$