# Math Help - Complex number question-

1. ## Complex number question-

If z(bar) = z , what can you say about z?

What exactly is teh question asking us- all i can come up with is- z(bar) is basically a rotation about the x-axis at teh same argumetn as z...

same modulus ??

what else ?

2. Originally Posted by Khonics89
If z(bar) = z , what can you say about z??
$\begin{gathered}
\overline {x + yi} = x - yi \hfill \\
\overline {3 - 4i} = 3 + 4i \hfill \\
\overline { - 1 - i} = - 1 + i \hfill \\
\overline {4i} = - 4i \hfill \\
\overline { - 7} = - 7 \hfill \\
\end{gathered}$

From these examples can you answer the question?

3. I know you get that minus sign ??

4. Originally Posted by Khonics89
I know you get that minus sign ??
The question is: "for what complex numbers is it true that $\overline z = z~?$"
What sort of numbers are left unchanged by taking the conguate?

5. the real parts ....

6. Originally Posted by Khonics89
the real parts ....
Exactly. If $z = \overline z$ then $z$ is a real number.
Or $\Im m(z) = 0$.