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受欢迎的代数 >

化简 (1/2+(sqrt(3))/2 i)^6

解答

化简

(\frac{1}{2} + \frac{3}{2} i)^{6}

解答

1

求解步骤

(\frac{1}{2} + \frac{3}{2} i)^{6}

使用二项式定理:

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

a = \frac{1}{2}, b = \frac{3}{2} i

= i = 0 \sum 6 (i 6) (\frac{1}{2})^{(6 - i)} (\frac{3}{2} i)^{i}

展开求和

= \frac{6 !}{0 ! ( 6 - 0 ) !} (\frac{1}{2})^{6} (\frac{3}{2} i)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (\frac{1}{2})^{5} (\frac{3}{2} i)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (\frac{1}{2})^{4} (\frac{3}{2} i)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (\frac{1}{2})^{3} (\frac{3}{2} i)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (\frac{1}{2})^{2} (\frac{3}{2} i)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (\frac{1}{2})^{1} (\frac{3}{2} i)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (\frac{1}{2})^{0} (\frac{3}{2} i)^{6}

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} (\frac{1}{2})^{6} (\frac{3}{2} i)^{0} : \frac{1}{64}

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} (\frac{1}{2})^{5} (\frac{3}{2} i)^{1} : \frac{3 3 i}{32}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} (\frac{1}{2})^{4} (\frac{3}{2} i)^{2} : \frac{45 i ^{2}}{64}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} (\frac{1}{2})^{3} (\frac{3}{2} i)^{3} : \frac{15 3 i ^{3}}{16}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} (\frac{1}{2})^{2} (\frac{3}{2} i)^{4} : \frac{135 i ^{4}}{64}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} (\frac{1}{2})^{1} (\frac{3}{2} i)^{5} : \frac{27 3 i ^{5}}{32}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} (\frac{1}{2})^{0} (\frac{3}{2} i)^{6} : \frac{27 i ^{6}}{64}

= \frac{1}{64} + \frac{3 3 i}{32} + \frac{45 i ^{2}}{64} + \frac{15 3 i ^{3}}{16} + \frac{135 i ^{4}}{64} + \frac{27 3 i ^{5}}{32} + \frac{27 i ^{6}}{64}

化简

\frac{1}{64} + \frac{3 3 i}{32} + \frac{45 i ^{2}}{64} + \frac{15 3 i ^{3}}{16} + \frac{135 i ^{4}}{64} + \frac{27 3 i ^{5}}{32} + \frac{27 i ^{6}}{64} : 1

= 1

流行的例子

化简 (-4/7)^4

s im pl i f y (- \frac{4}{7})^{4}

s im pl i f y a^{- 3}

8 x - 4 = 2 (3 x + 6)

因式分解 30y^2+10y-20

f a c t or 30 y^{2} + 10 y - 20

化简 e^{ln(4)}

s im pl i f y e^{l n (4)}