Complex number given:
$x = 1 + \cos \alpha + i \sin \alpha$
Desired form is something like $|x| \cdot e^{i \cdot \phi} = |x| \cdot (\cos \phi + i \sin \phi)$.
I somehow got completly stuck how to convert the number to the Euler style.
Maybe someone can help me.
I think I could write:
$x = \cos 0 + i\sin 0 + \cos \alpha + i \sin \alpha$
$x = (\cos 0 + \cos \alpha) + i (\sin 0 + \sin \alpha)$
Then $|x| = \sqrt{(\cos 0 + \cos \alpha)^2 + (\sin 0 + \sin \alpha)^2}$.
Is it then right to write $x = |x| \cdot e^{i \cdot \alpha} = \sqrt{(\cos 0 + \cos \alpha)^2 + (\sin 0 + \sin \alpha)^2} \cdot e^{i \cdot \alpha}$ ?
Is there a simpler way for the Euler style of $x$?