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$$4z^2+8|z|^2-3=0$$

I have to find $z$.

$|z|^2 = z\cdot \bar{z}$, but I don't know if this helps in this situation.

1 Answers 1

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You can prove first that $z^2$ is real, and then use the fact that $|z|^2=|z^2|$.

Can you find $z^2$ then?

  • 0
    How do I prove that $z^2$ is real?2011-11-03
  • 0
    can you see any reason why the second and third term would be real? (taking the conjugate also helps, but this is simpler)2011-11-03
  • 0
    So finally it will be $4z^2+8z^2-3=0$? Thank you!2011-11-03
  • 4
    Carefull, $z$ is complex, so $z^2$ can be also negative....2011-11-03
  • 1
    @nikita2 The last two are $\pm i \frac{\sqrt{3}}{2}$.2013-04-05
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    Answers: $z = \pm\frac12, \pm i\frac{\sqrt{3}}{2}$ (after corrections)2013-04-05