GraphingCalculator 4;
Window 65 46 720 1352;
PaneDivider 389;
FontSizes 16;
BackgroundType 0;
BackgroundColor 5 0 20;
StackPanes 1;
Slider 2 100;
SliderSteps 98;
SliderControlValue 98;
T -3.141592653589793 3.141592653589793;
U -3.141592653589793 3.141592653589793;
V -0 3.141592653589793;
4D.X -8 8;
4D.Y -8 8;
4D.Z -8 8;
4D.W -8 8;
4D.Show4DxyPlane 0;
4D.Show4Daxes 0;
4D.Depth 1.1930909743;
4D.View -0.7757304764114882 0.5529443296781996 0.1896641767934668 -0.2377441824300988 0.4117052807155325 0.8054371024697771 -0.17956618321484 0.3866856884338304 0.1322823339806737 -0.005296190105240481 0.9422182939507781 0.3077304356604434 0.4596111116031411 0.2132969587403302 0.2097812489994468 -0.8362140043363665;
4D.Speed1 0.2759055128302437;
4D.Speed2 0.2759055129622788;
4D.Axis1 0.8743522489010747 -0.2638932166978592 0.4072695851920321;
4D.Axis2 0.885555752597724 0.2399696043091234 0.397750673222311;
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 5;
MathPaneSlider 99;
Expr m=slider([-pi,pi+0.1]);
Color 7;
MathPaneSlider 200;
Expr l=slider([0,pi+0.1]);
MathPaneSlider 200;
Expr 'mred'=slider([-pi,pi]);
Color 2;
MathPaneSlider 200;
Expr 'lred'=slider([-pi,pi]);
Color 3;
MathPaneSlider 200;
Expr 'mblu'=slider([-pi,pi]);
Color 4;
MathPaneSlider 200;
Expr 'lblu'=slider([-pi-0.1,pi+0.1]);
Text "
COMPLEX COSINE w = cos z
z unit plane in green, w unit plane in magenta.
With parameter curves in blue and red.
With characteristic curves in yellow: showing real curves ""cos"" and ""sinh"" and 'cosh"" to be part of the same complex surface in different orientations.
Notice periodicity 2pi along x; -pi thru pi rendered here.
Try sliders m and l for surface rendering; 
mred thru lblu for parameter curve rendering.";
Color 7;
Expr vector(x,y,u,v)=vector(u,v,real(cos([u+i*v])),imag(cos([u+i*v]))),leq(0,v,l),leq(u,m);
Text "";
Color 6;
Grain 1;
Expr vector(x,y,u,v)=vector(u,-v,real(cos([u-(i*v)])),imag(cos([u-(i*v)]))),0<v<l,leq(u,m);
Color 3;
Expr vector(x,y,u,v)=vector(t,a*(pi/9),real(cos([t+i*a*(pi/9)])),imag(cos([t+i*a*(pi/9)]))),in(a,set(-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9)),leq(t,'mblu'),leq(a*(pi/9),'lblu');
Color 2;
Expr vector(x,y,u,v)=vector(a*(pi/9),t,real(cos([a*(pi/9)+i*t])),imag(cos([a*(pi/9)+i*t]))),in(a,set(-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,?)),leq(a*(pi/9),'mred'),leq(t,'lred');
Color 6;
Expr vector(x,y,u,v)=vector(t,0,real(cos([t])),0);
Color 6;
Expr vector(x,y,u,v)=vector(a,t,real(cos([a+i*t])),imag(cos([a+i*t]))),in(a,set(-pi,0,pi));
Color 6;
Expr vector(x,y,u,v)=vector(a,t,real(cos([a+i*t])),imag(cos([a+i*t]))),in(a,set(-pi/2,pi/2));
Color 4;
Expr vector(pi,0,0,0),vector(pi,pi,0,0),vector(0,pi,0,0),vector(0,0,0,0),vector(pi,0,0,0);
Expr vector(0,0,0,0),vector(0,0,pi,0),vector(0,0,pi,pi),vector(0,0,0,pi),vector(0,0,0,0);