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 0.4633452034148063 0.5674694483596293 -0.1520917400005836 0.663443856162893 -0.7162612452092089 0.6528938831020171 0.2463663879154815 -0.001734625613392195 0.3195635885293129 -0.006970191600626271 0.947539196718091 -1.430515731132969e-012 -0.412504744182508 -0.501656674449074 0.1354295987366689 0.7482240578860077;
4D.Speed1 0.1601219497242499;
4D.Speed2 0.1601219497242499;
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 127;
Expr m=slider([0.02,pi/2]);
Color 8;
MathPaneSlider 94;
Expr l=slider([-5,5]);
Color 2;
MathPaneSlider 200;
Expr 'mred'=slider([0.02,pi/2]);
Color 3;
MathPaneSlider 200;
Expr 'lred'=slider([-5,5]);
Color 4;
Expr 'mblu'=slider([0,pi/2]);
Color 7;
MathPaneSlider 200;
Expr 'lblu'=slider([-5,5]);
Text "
COMPLEX COSECANT w = cosec 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 ""cosec"" and ""sech"" and 'cosech"" to be part of the same complex surface in different orientations.
Notice asymptots z = 0 (""fanning"" blade) and w = 0 (""straight"" blades). Also, periodicity 2 pi along x; only a quarter 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(csc([u+i*v])),imag(csc([u+i*v]))),geq(u,m),leq(v,l);
Text "";
Color 3;
Expr vector(x,y,u,v)=vector(a,t,real(csc([a+i*t])),imag(csc([a+i*t]))),in(a,set(0.007,0.02,0.04,0.05,0.06,0.75,1,1.25,0.07000000000000001,0.08,0.12,0.14,0.16,0.2,0.25,0.3,0.4,0.5,0.1)),geq(a,'mblu'),leq(t,'lblu');
Color 2;
Expr vector(x,y,u,v)=vector(t,a,real(csc([t+i*a])),imag(csc([t+i*a]))),in(a,set(-5,-4,-3,-2,-1,-0.5,-0.3,-0.2,-0.15,-0.1,-0.08,-0.06,-0.04,-0.02,5,4,3,2,1,0.5,0.3,0.2,0.15,0.1,0.08,0.06,0.04,0.02)),leq(0<pi/2-t,'mred'),leq(a,'lred'*'µ');
Color 6;
Expr vector(x,y,u,v)=vector(0,t,real(csc([i*t])),imag(csc([i*t]))),-5<t<0;
Color 6;
Expr vector(x,y,u,v)=vector(0,t,real(csc([i*t])),imag(csc([i*t]))),0<t<5;
Color 6;
Expr vector(x,y,u,v)=vector(t,a,real(csc([t+i*a])),imag(csc([t+i*a]))),in(a,set(0)),0<t<pi/2;
Color 6;
Expr vector(x,y,u,v)=vector(a,t,real(csc([a+i*t])),imag(csc([a+i*t]))),in(a,set(pi/2));
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);
Color 5;
Expr vector(x,y,u,v)=vector(u/1.5,0.5+v/10,0,0);
Expr vector(x,y,u,v)=vector(0,0,u/1.5,0.5+v/10);