Вычислите: (2+i*sqrt12)^5

Решение в приложении.

(2+i√12)⁵    z=2+i√12   |z|=√4+12=√16=4 α=arctg √12/2=arctg 2√3/2=arctg √3=π/3 z=4(cosπ/3+isinπ/3) по теореме Муавра z⁵=4⁵(cos5π3-isin5π/3) cos 5π/3=cos(2π-5π/3)=cosπ/3    sin5π/3=-sin5π/3 z⁵=1024(cosπ3-isinπ3)=512-512√3i z⁵=4⁵(cos5π/3+isin5π/3)    cos5π/3=cos