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gennadiiyy
@gennadiiyy
July 2022
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выполнить действия ( комплексные числа)
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Dedagenn
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Обозначим u=(i/2+√3/2), z=u^12,
в тригонометрической форме |u|=√[(1/2²+ (-√3/2)²]=1, argu= π+ arctg((-1/2)/ (√3/2))= π-π/6=5π/6, u=1*(cos5π/6+isin5π/6). По формуле Муавра z=u^12=1^12* (cos(12*5*π/6)+isin(12*5*π/6))= 1*(cos10π+isin10π)= 1*(1+0)=1
Ответ z=1
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Verified answer
Обозначим u=(i/2+√3/2), z=u^12,в тригонометрической форме |u|=√[(1/2²+ (-√3/2)²]=1, argu= π+ arctg((-1/2)/ (√3/2))= π-π/6=5π/6, u=1*(cos5π/6+isin5π/6). По формуле Муавра z=u^12=1^12* (cos(12*5*π/6)+isin(12*5*π/6))= 1*(cos10π+isin10π)= 1*(1+0)=1
Ответ z=1