File:ComplexPolynomiaMapping3.svg
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Captions
Captions
Mapping of large circles by a complex polynomium
Summary[edit]
| Description |
Dansk: Til venstre: Tre cirkler med radier 11, 13 og 15 og centrum i 0 samt 18 punkter fordelt jævnt på periferien af den midterste cirkel og startende med det komplekse tal z = 12 – 5·i (markeret med grøn farve). Til højre: Billederne ved polynomiet P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) af cirkler og punkter. Billedkurven for cirklen med radius 13 går gennem origo, fordi P(12 – 5·i ) = 0.
English: Left: Three circles with radii 11, 13 and 15 and center 0 as well as 18 points distributed equally on the circumference of the middle circle and beginning with the complex number z = 12 – 5·i (marked with green color). Right: Images by the polynomium P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) of circles and points. The image of the circle with radius 13 passes through the origin, because P(12 – 5·i ) = 0.
Deutsch: Links: Drei Kreise mit den Radien 11, 13 und 15 und Mittelpunkt 0 sowie 18 Punkte gleichmäßig auf dem mittleren Kreis verteilt beginnend mit der komplexen Zahl z = 12 – 5·i (grün markiert). Rechts: Die Bildmengen des Polynoms P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) von Kreis und Punkte. Das Bild des Kreises mit radius 13 verläuft durch das Origo, weil P(12 – 5·i ) = 0. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:05, 18 December 2019 | | 638 × 306 (31 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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