How do you calculate $[3(cos14^circ+isin14^circ)]^4$ ?

Question

1412 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-09T21:27:56

$[3(cos14+isin14)]^4 =81(cos56+isin56)$

In order to solve this, we need to use Demoivre's theorem:

$[r( cosvartheta+isinvartheta)]^k = r^k(coskvartheta+isinkvartheta)$

$therefore[3(cos14+isin14)]^4 =3^4(cos(4*14)+isin(4*14))=81(cos56+isin56)$

How do you calculate [3(cos14^circ+isin14^circ)]^4[3(cos14^circ+isin14^circ)]^4?