Complex numbers: Solve the equation |z|^2 - Re(z^2) + iIm(iz) = 4 - 3i

[Qwertyuiop[]]

Hi, z is a complex number , solve the equation [imath]|\bar{z}|^2 - Re(z^2)+iIm(iz)= 4-3i[/imath]. This is what i found for :
[imath]|\bar{z}|^2: a^2 +b^2[/imath] , [imath]Re(z^2):a^2-b^2[/imath] and [imath]iIm(iz) :ai[/imath]. Solving the equation gives [imath]b=\pm\sqrt{2}[/imath] and [imath]a=-3[/imath] giving the 2 solutions as [imath]-3 + i\sqrt{2}[/imath] and [imath]-3-i\sqrt{2}[/imath]. Is my answer correct?

 

[blamocur]

Hi, z is a complex number , solve the equation [imath]|\bar{z}|^2 - Re(z^2)+iIm(iz)= 4-3i[/imath]. This is what i found for :
[imath]|\bar{z}|^2: a^2 +b^2[/imath] , [imath]Re(z^2):a^2-b^2[/imath] and [imath]iIm(iz) :ai[/imath]. Solving the equation gives [imath]b=\pm\sqrt{2}[/imath] and [imath]a=-3[/imath] giving the 2 solutions as [imath]-3 + i\sqrt{2}[/imath] and [imath]-3-i\sqrt{2}[/imath]. Is my answer correct?

Looks good to me.