簡約 [\sqrt[5]{3}((sqrt(3))/2+i/2)]^{10}

解

簡約

[53 (\frac{3}{2} + \frac{i}{2})]^{10}

\frac{9 ( 1 - 3 i )}{2}

解答ステップ

(53 (\frac{3}{2} + \frac{i}{2}))^{10}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(53 (\frac{3}{2} + \frac{i}{2}))^{10} = (53)^{10} (\frac{3}{2} + \frac{i}{2})^{10}

= (53)^{10} (\frac{3}{2} + \frac{i}{2})^{10}

(53)^{10} = 9

= 9 (\frac{3}{2} + \frac{i}{2})^{10}

簡素化

(\frac{3}{2} + \frac{i}{2})^{10} : \frac{1}{2} - \frac{3}{2} i

= \frac{1}{2} - \frac{3}{2} i

簡素化

9 (\frac{1}{2} - \frac{3}{2} i) : \frac{9 ( 1 - 3 i )}{2}

= \frac{9 ( 1 - 3 i )}{2}