<diagram dimensions="(300,300)" margins="5">
  <definition>
    alignments=['ne','ne','ne','nw','nw','sw','se','se']
  </definition>
  <definition substitution="no">
    labels=['1','\omega','i','\omega^3','-1','\omega^5','-i','\omega^7']
  </definition>
  <definition>f(t)=(cos(pi*t/4),sin(pi*t/4))</definition>
  <coordinates bbox="[-1.4,-1.4,1.4,1.4]">
    <grid at="grid" />
    <axes at="axes" labels="no" />
    <circle at="unit-circle" center="(0,0)" radius="1" stroke="blue"/>
    <repeat parameter="k=0..7">
      <point at="point" p="f(k)" alignment="alignments[k]">
        <m>${labels[k]}</m>
      </point>
    </repeat>
  </coordinates>

  <annotations>
    <annotation ref="figure" text="The eighth roots of unity">
      <annotation ref="axes" text="The coordinate axes" />
      <annotation ref="grid" text="The coordinate grid" />
      <annotation ref="unit-circle" text="The unit circle" circular="yes">
        <annotation ref="point-k=0" text="The primitive eighth root of unity to the power zero" speech="one"/>
        <annotation ref="point-k=1" text="The primitive eighth root of unity" speech="omega"/>
        <annotation ref="point-k=2" text="The primitive eighth root of unity squared" speech="i"/>
        <annotation ref="point-k=3" text="The primitive eighth root of unity cubed" speech="omega cubed"/>
        <annotation ref="point-k=4" text="The primitive eighth root of unity to the fourth" speech="minus one"/>
        <annotation ref="point-k=5" text="The primitive eighth root of unity to the fifth" speech="omega to the fifth"/>
        <annotation ref="point-k=6" text="The primitive eighth root of unity to the sixth" speech="minus i"/>
        <annotation ref="point-k=7" text="The primitive eighth root of unity to the seventh" speech="omega to the seventh"/>
      </annotation>
    </annotation>
  </annotations>

</diagram>
