Gegeben sei unten die komplexe Zahl \color{red}z .
Bewegen Sie den Punkt aus dem Ursprung zu \overline {\color{red}z}.
style({
stroke: "black",
strokeWidth: 2
});
graphInit({
range: [[-11, 11], [-9, 9]],
scale: [22, 22],
tickStep: 12,
labelStep: 10,
axisArrows: "->"
});
label([9.5,0], "\\operatorname{Re}", "above right");
label([0.1,7.5], "\\operatorname{Im}", "above right");
label( [X, Y], "\\color{red} \\large z", "left" );
circle( [X, Y], 3 / 15, {
fill: RED,
stroke: "none"
});
addMouseLayer();
graph.point = addMovablePoint({
coord: [ 0, 0 ],
snapX: 1,
snapY: 1
});
In der komplexen Zahlenebene bedeutet Konjugation einer komplexen Zahl z = {\color{orange}x} + { \color{blue}y}i
die Spiegelung an der x-Achse.
path([ [0,0], [X, 0]], {
stroke: ORANGE, strokeWidth: 4.5, strokeDasharray: "."
});
path([ [X, Y], [X, 0]], {
stroke: BLUE, strokeWidth: 3.2, strokeDasharray: "."
});
Dabei bleibt die x-Koordinate fest, und die y-Koordinate wechselt das Vorzeichen.
graph.re_point = addMovablePoint({
coord: [graph.point.coord[0], 0],
visible: false,
constraints: { fixed: true }
});
graph.im_point = addMovablePoint({
coord: [0, graph.point.coord[1]],
visible: false,
constraints: { fixed: true }
});
graph.re_line = addMovableLineSegment({
normalStyle: { stroke: BLUE },
pointA: graph.point,
pointZ: graph.re_point,
fixed: true
});
graph.im_line = addMovableLineSegment({
normalStyle: { stroke: ORANGE },
pointA: graph.point,
pointZ: graph.im_point,
fixed: true
});
graph.point.onMove = function(x, y) {
graph.re_point.setCoord([x, 0]);
graph.im_point.setCoord([0, y]);
graph.re_point.updateLineEnds();
graph.im_point.updateLineEnds();
return [x, y];
}