Задача 72199 (sqrt(2)-sqrt(6)i)^8...

62aaac79225ec1501a9067b6

02.07.2023 10:14:20

(sqrt(2)-sqrt(6)i)^8

5f3ea7e3faf909182968ddd9

02.07.2023 14:53:02

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[m]\sqrt{2}-\sqrt{6}i=\sqrt{2}\cdot (1-\sqrt{3}i)=\sqrt{2}\cdot 2\cdot (cos\frac{π}{3}-isin\frac{π}{3})[/m]

[m](\sqrt{2}-\sqrt{6}i)^{8}=(\sqrt{2})^{8}\cdot (1-\sqrt{3}i)^{8}=(\sqrt{2})^{8}\cdot 2^{8}\cdot (cos\frac{π}{3}-isin\frac{π}{3})^{8}=2^{12}\cdot (cos\frac{8π}{3}-isin\frac{8π}{3})=2^{12}\cdot (cos(2π+\frac{2π}{3})-isin(2π+\frac{2π}{3}))=[/m]

[m]=2^{12}\cdot (cos\frac{2π}{3}-isin\frac{2π}{3})=2^{11}(-1-\sqrt{3}i)=2048(-1-\sqrt{3}i)[/m]