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


Edit:

How about $$zz^*=1$$

  • 0
    Write $z=a+bi$ and what equation in $a,b$ do you get?2012-11-05
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    What do you mean by $zz*=1$=2012-11-05
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    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.

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    Second spite downvote I have gotten in two days. Hopefully this isn't a common thing...2012-11-05
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    Upvoted to spite them! Also, *this answer is useful...*2012-11-12