Why does current mathematics education often ignore the analyses of complex number solutions on (systems) of non-polynomial equations? [closed]

I have discovered that current mathematics education often teaches students to emphasize all polynomial equations should have complex solutions.

But starting from non-polynomial equations (e.g. $\sin x=x$), even in fact there are infinitely many complex solutions, the current mathematics education often teaches students to ignore them, even for the occasions on just needing the analyses of the number of the solutions. These attitudes make me upset as I for example feel that they have forgotten most transcendental functions are also defined in $\mathbb{C}$ and they are not respect the world of complex numbers.

• It's not entirely clear what you're asking for. Do you want ways to deal with this problem? Or do you want a historical explanation? Something else? – adamblan Mar 15 '14 at 21:52
• @adamblan: e.g. study the reasons of the particular phenomenon appearing in the current mathematics education. – doraemonpaul Mar 16 '14 at 1:11
• Why somebody want to close this question? Does Mathematics Educators SE really becomes the site which only welcome the mathematics educators' views on mathematics education but not welcome the students' views on mathematics education? – doraemonpaul Mar 16 '14 at 18:46
• @doraemonpaul I'm sorry this question was closed. Personally, my understanding is that we don't teach this because complex numbers simply make things more complex. At least, for the most part. But complex numbers are often unavoidable in polynomials. Often, it depends on the math course you are in. If it is a course that can avoid complex numbers all together, then it makes it easier for the students and the teachers. I have, in fact, found that I understand complex analysis a lot better than my teachers (high school). – Simply Beautiful Art Feb 3 '16 at 23:19

• If I am be the teacher, facing for solving e.g. $\sin x=x$ , I will teach my student that e.g. $x=a+bi$ , where $a$ and $b$ are the real solutions of $\begin{cases}a=\sin a\cosh b\\b=\cos a\sinh b\end{cases}$ , the trivial solution $x=0$ is the special case of $b=0$ . Plotting the complex plane of the system of equations will clearly show the pattern of the solutions of $\sin x=x$ . Showing them on textbooks are really difficult? – doraemonpaul Mar 15 '14 at 23:30