How many complex number satisfy $z\bar{z}=1$
Edit:
How about $zz^*=1$
How many complex number satisfy $z\bar{z}=1$
Edit:
How about $zz^*=1$
Infinitely many. If $z=x+iy$, $z\overline{z}=(x+iy)(x-iy)=x^{2}+y^{2}=|z|^{2}$, so you're asking how many $z$ satisfy $|z|=1$, which is every $z$ on the unit circle.
As many complex numbers as there are on the unit circle in the complex plane.