File:Complex fifth roots.svg

Basically, generated with the help of the following MetaPost code. Fixed some deficencies of SVG engine by hand.

% Some TeX abbreviations for conveniance verbatimtex \def\e#1{\sqrt[5]2 \cdot e^{\pi i/15 #1}} \def\en#1{\e{+2\pi i{#1}/5}} etex

% Unit length for drawings (not for TeX) u := 25mm;

% Radius of Circle r := 2**(1/5);

ru := 2*r*u;

% Bounding Box z.min = (-2.3,-1.5)*u; z.max = (2.2,2.1)*u;

pair s;

% Draw Background to ensure good Contrast fill for s = z.min, (x.max,y.min), z.max, (x.min,y.max):

  s-- endfor cycle withcolor (.99,.99,.99);

path p;

% Draw Circle p := fullcircle scaled ru;

draw p;

% Real Axis drawarrow (-2.1,0)*u--(2,0)*u; label.ulft(btex $\Re\mathrm e$ etex, (2,0)*u);

% Imag Axis drawarrow (0,-1.4)*u--(0,2)*u; label.llft(btex $\Im\mathrm m$ etex, (0,2)*u);

% Draw the 5th Roots as Arrows with Labels for i=0 upto 4:

  pair q;
  q := point 8*(1/30+i/5) of p;
  drawarrow (0,0)--q;
  if i=0:
     label.rt(btex $\e{}$ etex, q);
  elseif i=1:
     label.urt(btex $\en{}$ etex, q);
  elseif i=2:
     label.lft(btex $\en{\cdot 2}$ etex, q);
  elseif i=3:
     label.llft(btex $\en{\cdot 3}$ etex, q);
  else:
     label.lrt(btex $\en{\cdot 4}$ etex, q);
  fi;

endfor;

% Original Number we took the 5th Roots of s := (1,sqrt(3))*u; drawarrow (0,0)--s; label.rt(btex $1+i\sqrt3=2\cdot e^{\pi i/3}$ etex, s);

% Indicate "1" s := (u,0); d := 0.03u; draw ((0,-d)--(0,d)) shifted s withcolor black; label.llft(btex $1$ etex, s);

% Indicate Circle's Radius draw ((0,0)--(d,-d)) shifted (r*u,0) withcolor black; label.lrt(btex $\sqrt[5]2$ etex, (r,0)*u);