Use de moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

By De Moivre's theorem,

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let and let . Then recall that

On the left, so that

Since , we're left with

because we know to expect . Then from the Pythagorean identity, and knowing to expect , we get

Both and are -periodic, so that

and

so that the answer we left in trigonometric form above is equal to

c-   36

taxicab circle radius 9 has 4(9) = 36 points