Вычислите: (2+i*sqrt12)^5

Question

Вычислите:
(2+i*sqrt12)^5

Answer 1

(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

Answer 2

Решение в приложении.

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