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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 $\overline{-1 - i} = -1 + i$ ?

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  • $\begingroup$ 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. $\endgroup$ – user61527 Mar 24 '14 at 20:54
  • $\begingroup$ ah, so is my above example correct? / (-1 - i) = -1 + i. $\endgroup$ – user136088 Mar 24 '14 at 20:54
  • $\begingroup$ $\overline{a+ib} := a-ib$ $ \forall a,b \in \mathbb{R}$ $\endgroup$ – harry dunlop Mar 24 '14 at 20:55
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It just switches the sign of the imaginary part of the number. Your example is correct.

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