Plot of four fourth roots of (1-2i), then their cubes. 

>	with(plots):with(plottools):                                                                          # Load graphing libraries

 

>	C:=circle([0,0],5^(1/8),color=blue):                                                                  # Enter circle of R = eigth root of 5.

 

>	P:=line([0,0],[1,-2],color=red):                                                                      # Enter the point 1-2i.

 

>	R1:=line([0,0],[5^(1/8)*cos(-arctan(2)/4),5^(1/8)*sin(-arctan(2)/4)],color=purple);                   # Enter first root we found.

 

(1)

 

>	R2:=line([0,0],[5^(1/8)*cos(-arctan(2)/4+Pi/2),5^(1/8)*sin(-arctan(2)/4+Pi/2)],color=purple);         # Enter second root we found.

 

(2)

 

>	R3:=line([0,0],[5^(1/8)*cos(-arctan(2)/4+Pi),5^(1/8)*sin(-arctan(2)/4+Pi)],color=purple);             # Enter third root we found.

 

(3)

 

>	R4:=line([0,0],[5^(1/8)*cos(-arctan(2)/4+3*Pi/2),5^(1/8)*sin(-arctan(2)/4+3*Pi/2)],color=purple);     # Enter fourth toor we found.

 

(4)

 

>	display(C,P,R1,R2,R3,R4,view=[-2..2,-2..2]);                                                           # Plot all this!

 

Next we cube them. 

>	R13:=line([0,0],[5^(3/8)*cos(-3*arctan(2)/4),5^(3/8)*sin(-3*arctan(2)/4)],color=purple);

 

(5)

 

>	R23:=line([0,0],[5^(3/8)*cos(-3*arctan(2)/4+3*Pi/2),5^(3/8)*sin(-3*arctan(2)/4+3*Pi/2)],color=purple);

 

(6)

 

>	R33:=line([0,0],[5^(3/8)*cos(-3*arctan(2)/4+3*Pi),5^(3/8)*sin(-3*arctan(2)/4+3*Pi)],color=purple);

 

(7)

 

>	R43:=line([0,0],[5^(3/8)*cos(-3*arctan(2)/4+3*3*Pi/2),5^(3/8)*sin(-3*arctan(2)/4+3*3*Pi/2)],color=purple);

 

(8)

 

>	display(P,R13,R23,R33,R43,view=[-2..2,-2..2]);

 

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