# 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