Nombres complexes

Addition de nombres complexes 

<div id='box2' class='jxgbox' style='width:350px; height:350px;margin:auto;margin-top:10px; margin-bottom:10px;'></div>
<script type='text/javascript'>
var board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-6, 6, 6, -6], axis: true, showCopyright:false}); 
var org = board.create('point', [0,0], {style:10,visible:true,fixed:true,name:' '});
var x = board.create('point', [2,2], {style:5,color:'blue',name:'x'});
var y = board.create('point', [-1,-3], {style:5,color:'blue',name:'y'});
var xy = board.create('point', ["X(x)+X(y)","Y(x)+Y(y)"], {style:7,color:'green',name:'x+y'});
var ax =board.create('arrow', [org,x], {strokeColor:'blue'});
var ay =board.create('arrow', [org,y], {strokeColor:'blue'});
var axy =board.create('arrow', [org,xy], {strokeColor:'red'});
var ax2 =board.create('arrow', [x,xy], {strokeColor:'blue',strokeWidth:1,dash:1});
var ay2 =board.create('arrow', [y,xy], {strokeColor:'blue',strokeWidth:1,dash:1});
</script>

Multiplication de nombres complexes 

<div id='box3' class='jxgbox' style='width:350px; height:350px;margin:auto;margin-bottom:10px;'></div>
<script type='text/javascript'>
brd2 = JXG.JSXGraph.initBoard('box3', {boundingbox: [-6, 6, 6, -6], axis: true, showCopyright:false});    
var org2 = brd2.create('point', [0,0], {style:10,visible:true,fixed:true,name:' '});
var x = brd2.create('point', [1,0], {style:4,color:'blue',name:'x'});
var y = brd2.create('point', [0,2], {style:4,color:'red',strokeColor:'red',name:'y'});
var xy = brd2.create('point', ["X(x)*X(y)-Y(x)*Y(y)","X(x)*Y(y)+X(y)*Y(x)"], {style:7,fillColor:'green',strokeColor:'green',name:'x*y'});
var c = brd2.create('circle',[org2,1],{strokeWidth:1,dash:1});        
var ax =brd2.create('arrow', [org2,x], {strokeColor:'blue'});
var ax =brd2.create('arrow', [org2,y], {strokeColor:'red'});
var ax =brd2.create('arrow', [org2,xy], {strokeColor:'green'});
</script>

Plan complexe

 
<div id="jxgbox123" class="jxgbox" style="width:400px; height:400px;margin: auto;margin-top: 20px;margin-bottom:20px;"></div>
<script>
 var board = JXG.JSXGraph.initBoard('jxgbox123', {boundingbox: [-4, 4, 4, -4], axis: false, showNavigation: false, showCopyright: false, grid: true});
 JXG.Options.text.useMathJax = true;
 var absAxe = board.create('arrow',[ [-4,0],[4,0] ], {strokeColor: 'black', strokeWidth:2}); 
 var absOrd = board.create('arrow',[ [0,-4],[0,4] ], {strokeColor: 'black'});
 var vectU = board.create('arrow',[ [0,0],[1,0] ], {label:'u', strokeColor: 'black', strokeWidth:3});
 vectU.setProperty({fixed:true});
 var tu = board.create('text',[0.5,-0.3,function() { 
    return '$\\vec{u}$';
  }], {fontSize:12});
  tu.setProperty({fixed:true});
 var vectV = board.create('arrow',[ [0,0],[0,1] ], {strokeColor: 'black', strokeWidth:3});
 vectV.setProperty({fixed:true});
 var tv = board.create('text',[-0.4,0.5,function() { 
    return '$\\vec{v}$';
  }], {fontSize:12});
  tv.setProperty({fixed:true}); 
 var pO = board.create('point',[0,0], {name:'O',withLabel: true, label:{ offset:[-20,-10] } });
 pO.setProperty({fixed:true});
 var pM = board.create('point',[2.5,3],{name:'M',size:1});
 var pX = board.create('point',['X(M)',0],{name:'x',size:1});
 var pY = board.create('point',[0,'Y(M)'],{name:'y',size:1});
 var li1 = board.create('line',[pM,pX], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li2 = board.create('line',[pM,pY], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var v1 = board.create('arrow', [pO, pM], {strokeColor: 'blue', strokeWidth: '3px'});
 var t = board.create('text',['X(M)/2','Y(M)/2+0.3','r']);
 var tangle = board.create('angle', [[5,0],pO,pM], {type:'sector', orthoType:'square', orthoSensitivity:0, radius:0.5});
</script>

Plan complexe 2

 
<div id="jxgbox5123" class="jxgbox" style="width:400px; height:400px;margin: auto;margin-top: 20px;margin-bottom: 20px;"></div>
<script type="text/javascript">
 var board = JXG.JSXGraph.initBoard('jxgbox5123', {boundingbox: [-4, 4, 4, -4], axis: false, showNavigation: false, showCopyright: false, grid: true});
 JXG.Options.text.useMathJax = true;
 var absAxe = board.create('arrow',[ [-4,0],[4,0] ], {strokeColor: 'black', strokeWidth:2}); 
 var absOrd = board.create('arrow',[ [0,-4],[0,4] ], {strokeColor: 'black'});
 var vectU = board.create('arrow',[ [0,0],[1,0] ], {label:'u', strokeColor: 'black', strokeWidth:3});
 vectU.setProperty({fixed:true});
 var tu = board.create('text',[0.4,-0.15,function() { 
    return '$\\vec{u}$';
  }], {fontSize:12});
  tu.setProperty({fixed:true});
 var vectV = board.create('arrow',[ [0,0],[0,1] ], {strokeColor: 'black', strokeWidth:3});
 vectV.setProperty({fixed:true});
 var tv = board.create('text',[-0.4,0.5,function() { 
    return '$\\vec{v}$';
  }], {fontSize:12});
  tv.setProperty({fixed:true}); 
 var pO = board.create('point',[0,0], {name:'O',withLabel: true, label:{ offset:[-20,-10] } });
 pO.setProperty({fixed:true});
 var pM = board.create('point',[2.5,3],{name:'M',size:1});
 var pM1 = board.create('point',['X(M)','-Y(M)'],{name:'M\'',size:1});
 var pX = board.create('point',['X(M)',0],{name:'x',size:1});
 var pY = board.create('point',[0,'Y(M)'],{name:'y',size:1});
 var pY1 = board.create('point',[0,'-Y(M)'],{name:'-y',size:1}); 
 var li1 = board.create('line',[pM,pX], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li2 = board.create('line',[pM,pY], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li3 = board.create('line',[pM1,pY1], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li4 = board.create('line',[pM1,pX], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var v1 = board.create('arrow', [pO, pM], {strokeColor: 'blue', strokeWidth: '3px'});
 var v2 = board.create('arrow', [pO, pM1], {strokeColor: 'blue', strokeWidth: '3px'});
 var t = board.create('text',['X(M)/2','Y(M)/2+0.3','r']);
 var tangle = board.create('angle', [[5,0],pO,pM], {type:'sector', orthoType:'square', orthoSensitivity:0, radius:0.5});
 var tangle1 = board.create('angle', [pM1,pO,pX], {type:'sector', orthoType:'square', orthoSensitivity:0, radius:0.5, fillColor:'green'});
</script>

Plan complexe 3

 




<div id="jxgbox4" class="jxgbox" style="width:400px; height:400px;margin: auto;margin-top: 20px;margin-bottom: 20px;"></div>
<script type="text/javascript">
 var board = JXG.JSXGraph.initBoard('jxgbox4', {boundingbox: [-4, 4, 4, -4], axis: false, showNavigation: false, showCopyright: false, grid: true});
 JXG.Options.text.useMathJax = true;
 var absAxe = board.create('arrow',[ [-4,0],[4,0] ], {strokeColor: 'black', strokeWidth:2}); 
 var absOrd = board.create('arrow',[ [0,-4],[0,4] ], {strokeColor: 'black'});
 var vectU = board.create('arrow',[ [0,0],[1,0] ], {label:'u', strokeColor: 'black', strokeWidth:3});
 vectU.setProperty({fixed:true});
 var tu = board.create('text',[0.4,-0.15,function() { 
    return '$\\vec{u}$';
  }], {fontSize:12});
  tu.setProperty({fixed:true});
 var vectV = board.create('arrow',[ [0,0],[0,1] ], {strokeColor: 'black', strokeWidth:3});
 vectV.setProperty({fixed:true});
 var tv = board.create('text',[-0.4,0.5,function() { 
    return '$\\vec{v}$';
  }], {fontSize:12});
  tv.setProperty({fixed:true});  
 var pO = board.create('point',[0,0], {name:'O',withLabel: true, label:{ offset:[-20,-10] } });
 pO.setProperty({fixed:true});
 var pM = board.create('point',[2.5,3],{name:'M',size:1});
 var pM1 = board.create('point',['-X(M)','-Y(M)'],{name:'M\'',size:1});
 var pX = board.create('point',['X(M)',0],{name:'x',size:1});
 var pX1 = board.create('point',['-X(M)',0],{name:'-x',size:1});
 var pY = board.create('point',[0,'Y(M)'],{name:'y',size:1});
 var pY1 = board.create('point',[0,'-Y(M)'],{name:'-y',size:1});
 var li1 = board.create('line',[pM,pX], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li2 = board.create('line',[pM,pY], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li3 = board.create('line',[pM1,pY1], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var li4 = board.create('line',[pM1,pX1], {straightFirst:false, straightLast:false, strokeWidth:2, dash:2});
 var v1 = board.create('arrow', [pO, pM], {strokeColor: 'blue', strokeWidth: '3px'});
 var v2 = board.create('arrow', [pO, pM1], {strokeColor: 'blue', strokeWidth: '3px'});
 var t = board.create('text',['X(M)/2','Y(M)/2+0.3','r']);
 var tangle = board.create('angle', [[5,0],pO,pM], {type:'sector', orthoType:'square', orthoSensitivity:0, radius:0.5});
 var tangle1 = board.create('angle', [pM,pO,pM1], {type:'sector', orthoType:'square', orthoSensitivity:0, radius:0.5, fillColor:'green'});
</script>

Conjugué

 
<div id='box2uvw' class='jxgbox' style='width:400px; height:400px;margin:auto;margin-top:20px;margin-bottom: 20px;'></div> 
<script type='text/javascript'> 
JXG.Options.axis.ticks.drawLabels = false;
boardAZ = JXG.JSXGraph.initBoard('box2uvw', {boundingbox: [-2, 3, 5, -3], axis: true, showCopyright:false,showNavigation:false}); 
var pHaut = boardAZ.create('point', [3,2], {style:10,visible:true,name:'M a pour affixe z=x+iy',strokeColor:'blue',fillColor:'blue'});
var pBas = boardAZ.create('point', [function(){return pHaut.X()},function(){return -pHaut.Y()}], {style:10,visible:true,name:'M\' a pour affixe z=x-iy',strokeColor:'blue',fillColor:'blue'});
boardAZ.update();
</script>

Inégalité triangulaire

 
<div id="jxgbox6" class="jxgbox" style="width:400px; height:400px;margin: auto;margin-top: 20px;margin-bottom: 20px;"></div>
<script type="text/javascript">
 var board = JXG.JSXGraph.initBoard('jxgbox6', {boundingbox: [-2, 6, 6, -2], axis: false, showNavigation: false, showCopyright: false, grid: true});
 JXG.Options.text.useMathJax = true;
 var absAxe = board.create('arrow',[ [-2,0],[6,0] ], {strokeColor: 'black', strokeWidth:2}); 
 var absOrd = board.create('arrow',[ [0,-2],[0,6] ], {strokeColor: 'black'});
 var vectU = board.create('arrow',[ [0,0],[1,0] ], {label:'u', strokeColor: 'black', strokeWidth:3});
 vectU.setProperty({fixed:true});
 var tu = board.create('text',[0.5,-0.3,function() { 
    return '$\\vec{u}$';
  }], {fontSize:12});
  tu.setProperty({fixed:true});
 var vectV = board.create('arrow',[ [0,0],[0,1] ], {strokeColor: 'black', strokeWidth:3});
 vectV.setProperty({fixed:true});
 var tv = board.create('text',[-0.4,0.5,function() { 
    return '$\\vec{v}$';
  }], {fontSize:12});
  tv.setProperty({fixed:true}); 
 var pO = board.create('point',[0,0], {name:'O',withLabel: true, label:{ offset:[-20,-10] } });
 pO.setProperty({fixed:true});
 var pM = board.create('point',[2,3],{name:'M',size:1});
 var pMpr = board.create('point',[2.5,1],{name:'M\'',size:1});
 var pM1 = board.create('point',[ function () { return  pM.X()+pMpr.X() }, function () { return  pM.Y()+pMpr.Y() } ],{name:'M_1',size:1});
 var li1 = board.create('line',[pM,pO], { straightFirst:false, straightLast:false, strokeWidth:2});
 var li2 = board.create('line',[pMpr,pO], {straightFirst:false, straightLast:false, strokeWidth:2});
 var li1 = board.create('line',[pM1,pO], {straightFirst:false, straightLast:false, strokeWidth:2});
 var li1 = board.create('line',[pM,pM1], {straightFirst:false, straightLast:false, strokeWidth:2});
 var li1 = board.create('line',[pMpr,pM1], {straightFirst:false, straightLast:false, strokeWidth:2});
 var t1 = board.create('text', [function () { return  pM.X()/2-0.2 }, function () { return  pM.Y()/2+0.5 }, '|z|']);
 var t2 = board.create('text', [function () { return  pMpr.X()/2 }, function () { return  pMpr.Y()/2-0.2 }, '|z‘|']);
 var t3 = board.create('text', [function () { return  pM.X()+pMpr.X()/2 }, function () { return  pM.Y()+pMpr.Y()/2+0.5 }, '|z‘|']);
 var t4 = board.create('text', [function () { return  pM.X()/2+pMpr.X()/2-0.2 }, function () { return  pM.Y()/2+pMpr.Y()/2+0.4 }, '|z+z‘|']);
 var t5 = board.create('text', [function () { return  pM.X()/2+pMpr.X()+0.1 }, function () { return  pM.Y()/2+pMpr.Y() }, '|z|']);
</script>