### Home > PC3 > Chapter 11 > Lesson 11.2.5 > Problem11-144

11-144.

Use De Moivre’s Theorem to evaluate $( \operatorname { cos } ( \frac { \pi } { 12 } ) + i \operatorname { sin } ( \frac { \pi } { 12 } ) ) ^ { 6 }$.

Using the theorem, $r = 1$, $n = 6$, and $θ = π/12$.

$z^6=1^6\left( \cos\left(\frac{6\pi}{12}\right)+i\sin\left(\frac{6\pi}{12}\right) \right)$