A function $f$ is defined by $f(z)=i \bar{z}$. The number of values of $z$ that satisfy both $|z|=5$

Question

A function $f$ is defined by $f(z)=i \bar{z}$. The number of values of $z$ that satisfy both $|z|=5$ and $f(z)=z$ is

Professor PC Thomas Classes · Answer

$f(z) = z \Rightarrow i\bar{z} = z \Rightarrow i(x-iy) = x+iy \Rightarrow y+ix = x+iy \Rightarrow y=x$. Intersects $|z|=5$ at 2 points.