We know that the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
So, given a certain complex number, it is possibile to find its conjugate by writing it as:
Z = Re {Z} + j Im {Z}
and by considering:
Z* = Re {Z} – j Im {Z}
But in many applications (ex: signal theory etc) I saw people apply this rule: you have to replace "j" with "-j". Of course in case Z is written as shown before, it works. But in general?
For instance:
Z = (exp(4j)+sqrt(17j))/(exp(6j))
Best Answer
There are functions such that $(f(z))^*\neq f(z^*)$, for example, $$ f(z) = \mathrm{Re}z + \mathrm{Im}z.$$ However, if $f$ is analytic then the trick always works, i.e., $(f(z))^* = f(z^*)$. In your specific example the outcome will depend on how you choose to interpret the square root.