展開する (2.8455+1.1786i)^4

解

展開する

(2.8455 + 1.1786 i)^{4}

0.00482 \dots + 89.98359 \dots i

解答ステップ

(2.8455 + 1.1786 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 = 2.8455, b = 1.1786 i

= i = 0 \sum 4 (i 4) \cdot 2.845 5^{(4 - i)} (1.1786 i)^{i}

総和を展開する

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 2.845 5^{4} (1.1786 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 2.845 5^{3} (1.1786 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 2.845 5^{2} (1.1786 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 2.845 5^{1} (1.1786 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 2.845 5^{0} (1.1786 i)^{4}

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 2.845 5^{4} (1.1786 i)^{0} = 65.55930 \dots

簡素化

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 2.845 5^{3} (1.1786 i)^{1} : 108.61809 \dots i

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 2.845 5^{2} (1.1786 i)^{2} = - 67.48407 \dots

簡素化

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 2.845 5^{1} (1.1786 i)^{3} : - 18.63450 \dots i

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 2.845 5^{0} (1.1786 i)^{4} = 1.92959 \dots

= 65.55930 \dots + 108.61809 \dots i - 67.48407 \dots - 18.63450 \dots i + 1.92959 \dots

簡素化

65.55930 \dots + 108.61809 \dots i - 67.48407 \dots - 18.63450 \dots i + 1.92959 \dots : 0.00482 \dots + 89.98359 \dots i

= 0.00482 \dots + 89.98359 \dots i