Polarform (Cos, Sin) \(z = re^{i \varphi} = r (\cos(\varphi) + i \sin(\varphi)) \) schreiben.
Note 1: ETH::2. Semester::Analysis
Deck: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
ssuChhYL(+
Before
Front
Back
Polarform (Cos, Sin) \(z = re^{i \varphi} = r (\cos(\varphi) + i \sin(\varphi)) \) schreiben.
\[ e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \dots = \sum_{k = 0}^\infty \frac{1}{k!}x^k \]Setzen wir in diese formel \(x = it\) ein, so erhalten wir \(e^{it} = \cos(t) + i \sin(t)\), \(t \in \mathbb{R}\).
After
Front
Polarform (cosinus, sin) \(z = re^{i \varphi} = r (\cos(\varphi) + i \sin(\varphi)) \) schreiben.
Back
Polarform (cosinus, sin) \(z = re^{i \varphi} = r (\cos(\varphi) + i \sin(\varphi)) \) schreiben.
\[ e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \dots = \sum_{k = 0}^\infty \frac{1}{k!}x^k \]Setzen wir in diese formel \(x = it\) ein, so erhalten wir \(e^{it} = \cos(t) + i \sin(t)\), \(t \in \mathbb{R}\).
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | Polarform ( |
Polarform (cosinus, sin) \(z = re^{i \varphi} = {{c1:: r (\cos(\varphi) + i \sin(\varphi)) }}\) schreiben. |