let $z$ be a complex number and $\bar{z}$ it's conjugate ,i would like

to solve this equation :$$\bar{z}-iz²=-\sqrt{3}-3i$$ without using identity way ?

Note :by identity way the solution is clear and is: $z= -\sqrt{3}$

Thank you for any help

  • 1
    $\begingroup$ What is the "identity way"? $\endgroup$
    – Matthias
    Mar 20, 2016 at 13:49
  • $\begingroup$ I meant by identity way The real part of equality of RHS is the same the real part of the LHS ,the same with imaginary part $\endgroup$ Mar 20, 2016 at 13:51
  • $\begingroup$ You could do the same by using the absolute value and the argument. $\endgroup$
    – Matthias
    Mar 20, 2016 at 13:53

1 Answer 1


Hint you can do it by arguments . now argument if RHS is $2\pi-\tan^{-1}(\sqrt{3})=2\pi-\pi/3$ so argument of lhs needs to be the same so $\tan^{-1}(z^2/\bar{z})=2\pi-\pi/3$ but $z^2=z \times \bar{z}$ can you continue from here?

  • $\begingroup$ z^2=z \times \bar{z} ? I think |z|²=z \times \bar{z} $\endgroup$ Mar 20, 2016 at 14:08
  • $\begingroup$ I mean taking mode affect none so thought its understandable $\endgroup$ Mar 20, 2016 at 14:11
  • $\begingroup$ ah, sorry thanks $\endgroup$ Mar 20, 2016 at 14:13
  • $\begingroup$ No problem :).... $\endgroup$ Mar 20, 2016 at 14:22

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