Fundamental Theorem of Algebra illustration
- Author:
- ortollj
- Topic:
- Algebra
this litle Geogebra applet to illustrate the demonstration:
https://www.youtube.com/watch?v=shEk8sz1oOw
move slowly the slider Z_mod
####################Geogebra Algebra Fondamental Theorem demo test
#Slider( <Min>, <Max>, <Increment>, <Speed>, <Width>, <Is Angle>, <Horizontal>, <Animating>, <Random> )
a_0=Slider( -10, 10, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( a_0, 1, true )
SetValue( a_0, 7 )
b_0=Slider( -10, 10, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( b_0, 1, true )
######
SetValue( a_0, 7 )
SetValue( b_0, -7 )
z_0=a_0 + b_0*ί
SetColor( z_0, "red" )
######
a_1=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( a_1, 1, true )
b_1=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( b_1, 1, true )
###########
SetValue( a_1, 2 )
SetValue( b_1, 2 )
###########
z_1=a_1 + b_1*ί
######
a_2=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( a_2, 1, true )
b_2=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( b_2, 1, true )
z_2=a_2 + b_2*ί
######
SetValue( a_2, 2 )
SetValue( b_2, -2 )
######
a_3=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( a_3, 1, true )
b_3=Slider( -2, 2, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( b_3, 1, true )
z_3=a_3 + b_3*ί
######
SetValue( a_3, 2 )
SetValue( b_3, -2 )
maxZ=4
Z_{mod}=Slider( 0.01, maxZ, 0.01, 1, 100, false, true, false, true )
SetValue( Z_{mod}, 2.0 )
SetVisibleInView( Z_{mod}, 1, true )
a_z=Slider( -Z_{mod}, Z_{mod}, 0.01, 1, 100, false, true, false, true )
SetVisibleInView( a_z, 1, true )
signeOfa_z = RandomBetween[0, 1]
b_z=if[signeOfa_z==0,-sqrt(Z_{mod}^2-(a_z)^2), sqrt(Z_{mod}^2-(a_z)^2)]
######
degre=2
Z=a_z + b_z*ί
f=IF[degre<=2 ,z_2 * Z^2 +z_1 * Z + z_0,z_3*Z^3 + z_2 * Z^2 +z_1 * Z + z_0]
SetColor( f, "blue" )
Tracef = true