GraphingCalculator 4;
Window 65 46 720 1352;
PaneDivider 389;
FontSizes 16;
BackgroundType 0;
StackPanes 1;
SliderControlValue 1;
T -5 5;
U 0.02 1.5;
V -5 5;
4D.Show4DxyPlane 0;
4D.Show4Daxes 0;
4D.Depth 1.7330909743;
4D.View -0.05583507084220515 -0.08791282658366599 0.02945057007432554 0.9941259697337539 0.5960300032465979 -0.3700802463790799 -0.7122579964347284 0.02184932456220349 0.7621531924802204 -0.01607164488990876 0.6468155321551017 0.02222342870199477 0.2464816246370807 0.9246911097145829 -0.2710182241073375 0.1036449831128053;
4D.Speed1 0.2727076956241141;
4D.Speed2 0.2727076956241141;
4D.Axis1 0 0 -1;
4D.Axis2 0 0 -1;
Text "COMPLEX FUNCTIONS u+iv = w(x+iy) = w(z)
http://home.scarlet.be/~pin12499/qbComplex.html
by Guido 'wugi' Wuyts (Google wugi + qbcomplex)";
Color 7;
MathPaneSlider 33;
Expr m=slider([0.02,pi/2]);
Color 8;
MathPaneSlider 200;
Expr l=slider([-5,5]);
MathPaneSlider 200;
Expr 'mred'=slider([0.02,pi/2]);
Color 2;
MathPaneSlider 200;
Expr 'lred'=slider([-5,5]);
Color 3;
MathPaneSlider 200;
Expr 'mblu'=slider([0.02,pi/2]);
Color 4;
MathPaneSlider 200;
Expr 'lblu'=slider([-5,5]);
Text "
COMPLEX TANGENT w = tan z
z unit plane in cyan, w unit plane in magenta.
With parameter curves in blue and red.
With characteristic curves in yellow: showing real curves ""tan"" and ""tanh"" and 'cotanh"" to be part of the same complex surface in different orientations.
Notice the asymptots z = pi/2 (""fanning"" blade), w = 1 and w = -1 (""straight"" blades). Also, periodicity pi along x; only a half period 0 - pi/2 is rendered here.
Try sliders m and l for surface rendering; 
mred thru lblu for parameter curve rendering.
(Remark: the above surface function does not cover the fanning blade entirely and properly, as the parameter curves do. I couldn't fix that.)";
Color 12;
Expr vector(x,y,u,v)=vector(u,v,real(tan([u+i*v])),imag(tan([u+i*v]))),leq(u,m),leq(v,l);
Color 3;
Expr vector(x,y,u,v)=vector(a,t,real(tan([a+i*t])),imag(tan([a+i*t]))),in(a,set(0.1,0.25,0.5,0.75,1,1.2,1.3,1.4,1.42,1.44,1.46,1.48,1.5,1.52,1.53,1.54,1.55,1.56,1.35)),leq(a,'mblu'),leq(t,'lblu');
Color 2;
Expr vector(x,y,u,v)=vector(t,a,real(tan([t+i*a])),imag(tan([t+i*a]))),in(a,set(-5,-4,-3,-2,-1,-0.5,-0.25,-0.2,-0.15,-0.1,-0.08,-0.06,-0.04,-0.02,5,4,3,2,1,0.5,0.25,0.2,0.15,0.1,0.08,0.06,0.04,0.02)),leq(0<t,'mred'),leq(a,'lred'*'µ');
Color 6;
Expr vector(x,y,u,v)=vector(0,t,real(tan([i*t])),imag(tan([i*t]))),-5<t<0;
Color 6;
Expr vector(x,y,u,v)=vector(0,t,real(tan([i*t])),imag(tan([i*t]))),0<t<5;
Color 6;
Expr vector(x,y,u,v)=vector(t,a,real(tan([t+i*a])),imag(tan([t+i*a]))),in(a,set(0)),0<t<pi/2;
Color 6;
Expr vector(x,y,u,v)=vector(pi/2,t,real(tan([pi/2+i*t])),imag(tan([pi/2+i*t]))),-5<t<0;
Color 6;
Expr vector(x,y,u,v)=vector(pi/2,t,real(tan([pi/2+i*t])),imag(tan([pi/2+i*t]))),5>t>0;
Color 5;
Expr vector(0,0,0,0),vector(1,0,0,0),vector(1,1,0,0),vector(0,1,0,0),vector(0,0,0,0);
Expr vector(0,0,0,0),vector(0,0,1,0),vector(0,0,1,1),vector(0,0,0,1),vector(0,0,0,0);