Perimeters of Polygons

Question

A. Calculate the perimeter of the polygon whose vertices are the complex fourth roots of 1.

B. Calculate the perimeter of the polygon whose vertices are the complex ninth roots of 1.

 

 

Answer 1

A.

The four complex roots are 1, i, -1, -i

Plot these points.

The distance between each is √2

So what is the perimeter?

B.

This is very, very messy

The first ninth root is 1

The second ninth root is

cos 2π/9 + i sin 2π/9

0.975414982 + 0.220376067 i

Now if you really, really want to continue

Determine the distance between

(1, 0) and (0.975414982, 0.220376067)

And multiply by 9.