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How many complex number satisfy $z\bar{z}=1$


Edit:

How about $zz^*=1$

  • 0
    I guess $z^*$ is physics notation for the complex conjugate.2012-11-05

2 Answers 2

8

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.

5

As many complex numbers as there are on the unit circle in the complex plane.

  • 1
    Upvoted to spite them! Also, *this answer is useful...*2012-11-12