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受欢迎的 >

3(cos(pi/4)+isin(pi/4))

解答

3 (cos (\frac{π}{4}) + i sin (\frac{π}{4}))

解答

\frac{3 2}{2} + i \frac{3 2}{2}

求解步骤

3 (cos (\frac{π}{4}) + i sin (\frac{π}{4}))

使用以下普通恒等式:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

使用以下普通恒等式:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 3 (\frac{2}{2} + i \frac{2}{2})

化简

3 (\frac{2}{2} + i \frac{2}{2}) : \frac{3 2}{2} + i \frac{3 2}{2}

3 (\frac{2}{2} + i \frac{2}{2})

乘

i \frac{2}{2} : \frac{2 i}{2}

i \frac{2}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 i}{2}

= 3 (\frac{2 i}{2} + \frac{2}{2})

化简

\frac{2}{2} + \frac{2 i}{2} : \frac{2 + 2 i}{2}

\frac{2}{2} + \frac{2 i}{2}

使用法则

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 + 2 i}{2}

= 3 \cdot \frac{2 + 2 i}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 2 + 2 i ) \cdot 3}{2}

分解

2 + 2 i : 2 (1 + i)

2 + 2 i

因式分解出通项

2

= 2 (1 + i)

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

消掉

\frac{2 ( 1 + i ) \cdot 3}{2} : \frac{( 1 + i ) \cdot 3}{2}

\frac{2 ( 1 + i ) \cdot 3}{2}

使用根式运算法则:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

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

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

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

数字相减:

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

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

使用根式运算法则:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

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

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

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

有理化:

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

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

乘以共轭根式

\frac{2}{2}

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

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

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

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

将

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

改写成标准复数形式:

\frac{3 2}{2} + \frac{3 2}{2} i

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

使用根式运算法则:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

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

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

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

数字相减:

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

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

使用根式运算法则:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

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

乘开

3 (1 + i) : 3 + 3 i

3 (1 + i)

使用分配律:

a (b + c) = ab + a c

a = 3, b = 1, c = i

= 3 \cdot 1 + 3 i

数字相乘:

3 \cdot 1 = 3

= 3 + 3 i

= \frac{3 + 3 i}{2}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3 + 3 i}{2} = \frac{3}{2} + \frac{3 i}{2}

= \frac{3}{2} + \frac{3 i}{2}

\frac{3}{2} = \frac{3 2}{2}

\frac{3}{2}

乘以共轭根式

\frac{2}{2}

= \frac{3 2}{2 2}

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{3 2}{2}

= \frac{3}{2} + \frac{3 2}{2} i

\frac{3}{2} = \frac{3 2}{2}

\frac{3}{2}

乘以共轭根式

\frac{2}{2}

= \frac{3 2}{2 2}

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{3 2}{2}

= \frac{3 2}{2} + \frac{3 2}{2} i

= \frac{3 2}{2} + \frac{3 2}{2} i

= \frac{3 2}{2} + i \frac{3 2}{2}

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