I'd like to check my result.
Find all the complex numbers such that .
I've found that , where . So when is any real number.
Actually it is if , then while
because in the right hand it is and not
even if it is the same since
\cos x - i \sin x)" alt="\overline{e^{iz}} = \overline{e^{i(x+iy)}} = \overline{e^{-y}e^{ix}} = e^{-y}\\cos x - i \sin x)" /> while
\cos x - i \sin x)" alt="e^{\overline{iz}} = e^{-i \overline{z}} = e^{-i (x-iy)} = e^{-y}\\cos x - i \sin x)" />