Bewegen Sie den Punkt aus dem Ursprung zu der komplexen Zahl z = X + Yi
in der komplexen Zahlenebene.
style({
stroke: "black",
strokeWidth: 2
});
graphInit({
range: [[-11, 11], [-9, 9]],
scale: [22, 22],
tickStep: 2,
labelStep: 1,
axisArrows: "->"
});
label([-2,0], "\\llap{-}2", "below");
label([0,-2], "\\llap{-}2", "left");
label([9.5,0], "\\operatorname{Re}", "above right");
label([0.1,7.5], "\\operatorname{Im}", "above right");
addMouseLayer();
graph.point = addMovablePoint({
coord: [ 0, 0 ],
snapX: 1,
snapY: 1
});
In der komplexen Zahlenebene finden wir eine Zahl z = {\color{orange}x} + {\color{blue}y}i
als Punkt mit den Koordinaten ({\color{orange}x},{\color{blue}y}).
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];
}
Hier ist z = {\color{orange}X} { \color{blue} + Y}i.
Wir bewegen den Punkt an die Stelle ({\color{orange}X}, {\color{blue}Y}).