Question

((2(cos60+isin60))^4
C решениееем!!

Answer 1

Формула Муавра:

$\boxed {\; z^{n}=|z|^{n}\cdot \Big (cos(n\varphi )+i\, sin(n\varphi )\Big )\, }\\\\\\z=2\, (cos\, 60^\circ +i\, sin60^\circ )\\\\z^{4}=2^4\cdot (cos240^\circ +i\, sin240^\circ )\\\\cos240^\circ =cos(360^\circ -120^\circ )=cos(-120^\circ )\; \; ,\; \; -180^\circ <-120^\circ \leq 180^\circ \; ,\\\\\\z^4=16\cdot \Big (cos(-120^\circ )+i\, sin(-120^\circ )\Big )$