Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm not sure about the the normal vectorNon a complex function

[tex] z(x,t) = A e^{i(\omega t + \alpha x)} [/tex]

My approach is that ([itex]\overline{z}[/itex] beeing the conjugate of [itex]z[/itex]):

[tex]

\Re{(\mathbf{N})} = \frac{1}{\sqrt{\frac{1}{4}(\partial x + \overline{\partial x} )^2 + \frac{1}{4}(\partial z + \overline{\partial z} )^2 }} \begin{bmatrix}

-\frac{1}{2}(\partial z + \overline{\partial z}) \\

\frac{1}{2}(\partial x + \overline{\partial x})

\end{bmatrix}

[/tex]

and

[tex]

\Im{(\mathbf{N})} = \frac{1}{\sqrt{-\frac{1}{4}(\partial x - \overline{\partial x} )^2 -\frac{1}{4}(\partial z - \overline{\partial z} )^2 }} \begin{bmatrix}

-\frac{1}{2i}(\partial z - \overline{\partial z}) \\

\frac{1}{2i}(\partial x - \overline{\partial x})

\end{bmatrix}

[/tex]

So I have [itex] \frac{\partial z}{\partial x} = i\omega A e^{i(\omega t + \alpha x)} [/itex]. Do I now choose [itex]\partial x = 1 + i[/itex] for the complex x-component? Can I see the imaginary part of the normal vector as the normal vector on the imaginary part of z? Or is my approach wrong?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Normal vector on complex function

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**