File:ComplexExpMapping.svg
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Captions
Captions
Mapping of the complex plane by the exponential function
Summary[edit]
| Description |
Dansk: Illustration af den komplekse eksponentialfunktions afbildning af det komplekse plan, w = exp(z) . Til venstre: z-planet med de tre komplekse tal 0, 1, og i, et kvadratisk net med maskestørrelse 1, en del af den vandrette stribe –π < Im(z) < π (markeret med en lysegrå baggrund) samt to rektangler med grøn og magenta farve. Til højre: Exp-billederne af disse objekter: Vandrette linier afbildes i halvlinier, som udgår fra 0, lodrette i cirkler med centrum i 0. De danner kurveskarer, som lokalt står vinkelret på hinanden. Tallet w = 0 er som det eneste ikke et billedpunkt.
English: Illustration of the mapping of the complex plane by the complex exponential function, w = exp(z). Left:The z-plane with the three complex numbers 0, 1, and i, a quadratic net with mesh size 1, part of the horizontal stripe –π < Im(z) < π (marked with a light gray background) as well as two rectangles colored green and magenta. Right: The images of these objects by the exponential function: Horizontal lines are mapped onto halflines emerging from 0, vertical ones onto circles with center 0. They form curves which locally intersect each other perpendicularly. The number w = 0 is the only one which is not an image point.
Deutsch: Darstellung der Abbildung der komplexen Ebene durch die komplexe Exponentialfunktion, w = exp(z). Links: Die z-Ebene mit den drei komplexen Zahlen 0, 1, und i, ein quadratisches Netz mit einer Maschenweite von 1, ein Teil des waagerechten Streifens –π < Im(z) < π (hellgrau hinterlegt) sowie zwei Grün und Magenta gefärbte Rechtecke. Rechts: Die Exp-Bilder dieser Objekte: Horizontale Linien werden Halblinie, welche von 0 ausstrahlen, abgebildet, vertikale Kreise mitMittelpunkt 0. Sie bilden lokal senkrecht zueinander stehende Kurven. Die Zahl w = 0 ist als einzige kein Bildpunkt. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:19, 18 December 2019 | | 638 × 306 (27 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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