Answer
We can draw the eighth roots of 1 on the complex plane.
Connecting the tips of these eight vectors will give us a regular octagon.
Work Step by Step
An octagon has 8 sides.
$\frac{360^{\circ}}{8} = 45^{\circ}$
We can draw the eighth roots of 1 on the complex plane:
$cos~0^{\circ}+~i~sin~0^{\circ}$
$cos~45^{\circ}+~i~sin~45^{\circ}$
$cos~90^{\circ}+~i~sin~90^{\circ}$
$cos~135^{\circ}+~i~sin~135^{\circ}$
$cos~180^{\circ}+~i~sin~180^{\circ}$
$cos~225^{\circ}+~i~sin~225^{\circ}$
$cos~270^{\circ}+~i~sin~270^{\circ}$
$cos~315^{\circ}+~i~sin~315^{\circ}$
Connecting the tips of these eight vectors will give us a regular octagon.
