Prove that if z is a complex number then $\overline{\overline{z}}=z$

Question

So I started off my stating that $z=a+bi$ and $\overline{z}=a-bi$. Then take the conjugate of the conjugate and we get $\overline{\overline{z}}$= $\overline{a-bi}=a+bi$.

Now I'm not sure if this is 100% correct, or that writing a proof like this is correct. If anyone could point me in the right direction please let me know. Thank you.

Answer 1

Geometric proof: the conjugation is the symmetry about the horizontal axis. This symmetry is obviously idempotent.