File:ComplexCosMapping.svg
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Size of this PNG preview of this SVG file: 638 × 306 pixels. Other resolutions: 320 × 153 pixels | 640 × 307 pixels | 1,024 × 491 pixels | 1,280 × 614 pixels | 2,560 × 1,228 pixels.
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Captions
Captions
Mapping of the complex plane by the cosine function
Summary[edit]
| Description |
Dansk: Illustration af den komplekse cosinus-funktions afbildning af det komplekse plan, w = cos(z). Til venstre: z-planet med de fire komplekse tal 0, 1, i og 1 + i, et kvadratisk net med maskestørrelse 0.5, en del af den lodrette stribe –π < Re(z) < π (markeret med en lysegrå baggrund) samt to rektangler med grøn og cyan farve. Til højre: Cosinus-billedet af disse objekter: Vandrette linier afbildes i ellipser, lodrette i hyperbler, der alle har brændpunkter i –1 og 1. De danner kurveskarer, som lokalt står vinkelret på hinanden.
English: Illustration of the mapping of the complex plane by the complex cosine function, w = cos(z). Left:The z-plane with the four complex numbers 0, 1, i and 1 + i, a quadratic net with mesh size 0.5, part of the vertical stripe –π < Re(z) < π (marked with a light gray background) as well as two rectangles colored green and cyan. Right: The cosine images of these objects: Horizontal lines are mapped onto ellipses, vertical ones onto hyperbolas, all of which have focal points at –1 and 1. They form curves which locally intersect each other perpendicularly.
Deutsch: Darstellung der Abbildung der komplexen Ebene durch die komplexe Kosinusfunktion, w = cos (z). Links: Die z-Ebene mit den vier komplexen Zahlen 0, 1, i und 1 + i, ein quadratisches Netz mit einer Maschenweite von 0,5, ein Teil des senkrechten Streifens –π < Re(z) < π (hellgrau hinterlegt) sowie zwei Rechtecke mit grüner und cyaner Farbe. Rechts: Das Kosinus-Bild dieser Objekte: Horizontale Linien werden in Ellipsen abgebildet, vertikale in Hyperbeln, die sämtlich Brennpunkte in –1 und 1 besitzen. Sie bilden lokal senkrecht zueinander stehende Kurven. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:19, 18 December 2019 | | 638 × 306 (41 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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