展開する (9.3+2.1i)^4

解

展開する

(9.3 + 2.1 i)^{4}

5211.4428 + 6412.0896 i

解答ステップ

(9.3 + 2.1 i)^{4}

2項定理を適用する:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 9.3, b = 2.1 i

= i = 0 \sum 4 (i 4) \cdot 9. 3^{(4 - i)} (2.1 i)^{i}

総和を展開する

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 9. 3^{4} (2.1 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 9. 3^{3} (2.1 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 9. 3^{2} (2.1 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 9. 3^{1} (2.1 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 9. 3^{0} (2.1 i)^{4}

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 9. 3^{4} (2.1 i)^{0} = 7480.5201

簡素化

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 9. 3^{3} (2.1 i)^{1} : 6756.5988 i

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 9. 3^{2} (2.1 i)^{2} = - 2288.5254

簡素化

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 9. 3^{1} (2.1 i)^{3} : - 344.5092 i

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 9. 3^{0} (2.1 i)^{4} = 19.4481

= 7480.5201 + 6756.5988 i - 2288.5254 - 344.5092 i + 19.4481

簡素化

7480.5201 + 6756.5988 i - 2288.5254 - 344.5092 i + 19.4481 : 5211.4428 + 6412.0896 i

= 5211.4428 + 6412.0896 i