Show that $v + iu$ is the reflection of the point $u + iv$ across the line $u = v$

Question

Show that $v + iu$ is the reflection of the point $u + iv$ across the line $u = v$

My attempt :I know that the reflection of the point $(x,y)$ across the line $y = x $ is the point $(y, x)$

i,e line of equation will be $x-y=0$

But here im confused that how to show $v + iu$ is the reflection of the point $u + iv$

Answer 1

You pretty much have it. If you know that the reflection of $(x,y)$ across $x=y$ is $(y,x)$, then just note that we identify $a+bi$ with $(a,b)$ when we identify $\Bbb{C}\cong \Bbb{R}^2$. In particular, the reflection across $x=y$ sends $a+bi$ to $b+ai$.