## Example 1.2.17 (a): Finding roots geometrically |

Find the cube roots of |

With *8 = 8 cis(0)* the formula gives us three roots:

z_{1}= 2 cis(0/3) = 2z_{2}= 2 cis((0 + 2)/3) = 2 cis(2/3)z_{3}= 2 cis((0 + 4)/3) = 2 cis(4/3)

But it's more fun to do this geometrically. We have *8 = 8 cis(0)*.

**Step 1: Draw the vector 8**

a = 8

**Step 2: Divide the angle by 3 and adjust the lengh**

z_{1}= 2

**Step 3: Draw 3 equally spaced segments, starting at the first root**

z_{1}= 2z_{2}= 2 cis(2/3)z_{3}= 2 cis(4/3)

We already figured out the three third roots of *i* so we won't
have to do that again.