化简 (1-(3+i)^2(1-2i))/(2i^{77)-i^{726}}

解答

化简

\frac{1 - ( 3 + i ) ^{2} ( 1 - 2 i )}{2 i ^{77} - i ^{726}}

\frac{1}{5} + i \frac{48}{5}

求解步骤

\frac{1 - ( 3 + i ) ^{2} ( 1 - 2 i )}{2 i ^{77} - i ^{726}}

2 i^{77} - i^{726} = 2 i + 1

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

(3 + i)^{2} (1 - 2 i) = 20 - 10 i

= \frac{1 - ( 20 - 10 i )}{2 i + 1}

使用复数算数法则:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = - 19, b = 10, c = 1, d = 2

= \frac{( - 19 \cdot 1 + 10 \cdot 2 ) + ( 10 \cdot 1 - ( - 19 ) \cdot 2 ) i}{1 ^{2} + 2 ^{2}}

整理后得

= \frac{1 + 48 i}{5}

将

\frac{1 + 48 i}{5}

改写成标准复数形式:

\frac{1}{5} + \frac{48}{5} i

= \frac{1}{5} + \frac{48}{5} i

s im pl i f y \frac{74}{1.6 5 ^{2}}

f a c t or x y + 4 x y^{2}

s im pl i f y \frac{cos ( x )}{sin ^{2} ( x )}

s im pl i f y (x + 3) (x + 5) - (x + 10) (x - 2)

s im pl i f y \frac{cos ^{2} ( x )}{sin ^{2} ( x )}