# Does the complex conjugate just switch the sign in-between the numbers?

I have a question about imaginary numbers and their complex conjugate.

My teacher denotes the complex conjugate to have a bar over it. For example: $\overline{3+5i} = 3 - 5i$

But does the complex conjugate just switch the sign in-between the numbers?

For example, would $\overline{-1 - i} = -1 + i$ ?

• The complex conjugate of the complex number $a + bi$ is, by definition, the complex number $a - bi$. It changes the sign on the imaginary component only. – user61527 Mar 24 '14 at 20:54
• ah, so is my above example correct? / (-1 - i) = -1 + i. – user136088 Mar 24 '14 at 20:54
• $\overline{a+ib} := a-ib$ $\forall a,b \in \mathbb{R}$ – harry dunlop Mar 24 '14 at 20:55