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

${\left[3 \left(\cos 14 + i \sin 14\right)\right]}^{4} = 81 \left(\cos 56 + i \sin 56\right)$
${\left[r \left(\cos \vartheta + i \sin \vartheta\right)\right]}^{k} = {r}^{k} \left(\cos k \vartheta + i \sin k \vartheta\right)$
$\therefore {\left[3 \left(\cos 14 + i \sin 14\right)\right]}^{4} = {3}^{4} \left(\cos \left(4 \cdot 14\right) + i \sin \left(4 \cdot 14\right)\right) = 81 \left(\cos 56 + i \sin 56\right)$