File:ComplexPolynomiaMapping.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.
Original file (SVG file, nominally 638 × 306 pixels, file size: 26 KB)
Captions
Captions
Mapping by a complex polynomium
Summary[edit]
| Description |
Dansk: Til venstre: En cirkel med radius 5 og centrum i 0 samt 18 punkter fordelt jævnt på periferien og startende med det komplekse tal z = 3 + 4·i (markeret med grøn farve). Til højre: Billedet ved polynomiet P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) af cirkel og punktrække. Billedkurven går gennem origo, fordi P(3 + 4·i) = 0, dvs. 3 + 4·i er en rod i polynomiet.
English: Left: A circle with radius 5 and center at 0 as well as 18 points distributed equally on the circumference and beginning with the complex number z = 3 + 4·i (marked with green color). Right: Images by the polynomium P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) of circle and points. The image curve passes through the origin because P(3 + 4·i) = 0, i. e. 3 + 4·i is a root of the polynomium.
Deutsch: Links: Ein Kreis mit Radius 5 und Mittelpunkt 0 sowie 18 gleichmäßig auf dem Kreis verteilten Punkte, beginnend mit der komplexen Zahl z = 3 + 4·i (grün markiert). Rechts: Die Bildmengen des Polynoms P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) von Kreis und Punkte. Die Bildkurve verläuft durch das Origo, weil P(3 + 4·i) = 0, d.h. 3 + 4·i ist eine Wurzel des Polynoms. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:05, 18 December 2019 | | 638 × 306 (26 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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