Python中的复数？

2024-04-24 01:03:03 216

从实数创建复数。可以使用直接赋值语句或使用complex()函数来创建Python复数。

复数通常在我们使用两个实数的地方使用。例如，由电压(V)和电流(C)定义的电路被用于几何学，科学计算和微积分中。

语法

complex([real[, imag]])

在python中创建一个简单的复数

>>> c = 3 +6j
>>> print(type(c))
<class 'complex'>
>>> print(c)
(3+6j)
>>>
>>> c1 = complex(3,6)
>>> print(type(c1))
<class 'complex'>
>>> print(c1)
(3+6j)

从以上结果中，我们可以看到python复数是complex类型。每个复数由一个实部和一个虚部组成。

Python复数-属性和函数

>>> #Complex Number:
>>> c = (3 + 6j)
>>>
>>> #Real Part of complex number
>>> print('Complex Number: Real Part is = ', c. real)
Complex Number: Real Part is = 3.0
>>>
>>> #Imaginary Part of complex number
>>> print('Complex Number: Imaginary Part is = ', c. imag)
Complex Number: Imaginary Part is = 6.0
>>>
>>> #Conjugate of complex number
>>> print('Complex Number: conjugate Part = ', c. conjugate())
Complex Number: conjugate Part = (3-6j)

复数的数学计算

我们可以对复数进行简单的数学计算：

>>> #first complex number
>>> c1 = 3 + 6j
>>> #Second complex number
>>> c2 = 6 + 15j
>>>
>>> #Addition
>>> print("Addition of two complex number =", c1 + c2)
Addition of two complex number = (9+21j)
>>>
>>> #Subtraction
>>> print("Subtraction of two complex number =", c1 - c2)
Subtraction of two complex number = (-3-9j)
>>>
>>> #Multiplication
>>> print("Multiplication of two complex number =", c1 * c2)
Multiplication of two complex number = (-72+81j)
>>>
>>> #Division
>>> print("Division of two complex number =", c1 / c2)
Division of two complex number = (0.4137931034482759-0.03448275862068964j)

但是，复数不支持<，>，<=，=>之类的比较运算符，它将通过TypeError消息显示：

>>> c2 <= c2
Traceback (most recent call last):
File "<pyshell#40>", line 1, in <module>
c2 <= c2
TypeError: '<=' not supported between instances of 'complex' and 'complex'

Pythoncmath模块

Pythoncmath模块提供对复数数学函数的访问。让我们使用数学模块功能查看复数的一些重要功能。

复数相位

复数的相位是实轴与代表虚部的向量之间的夹角。

math和cmath模块返回的相位以弧度表示，我们使用numpy.degrees()函数将其转换为度。

import cmath, math, numpy
c = 4+ 4j
# phase
phase = cmath.phase(c)
print('4+ 4j Phase =', phase)
print('Phase in Degrees =', numpy.degrees(phase))
print('-4-4j Phase =', cmath.phase(-4-4j), 'radians. Degrees =', numpy.degrees(cmath.phase(-4-4j)))
# we can get phase using math.atan2() function too
print('Complex number phase using math.atan2() =', math.atan2(2, 1))

结果

4+ 4j Phase = 0.7853981633974483
Phase in Degrees = 45.0
-4-4j Phase = -2.356194490192345 radians. Degrees = -135.0
Complex number phase using math.atan2() = 1.1071487177940904

cmath模块常量

cmath模块中有几个常量可用于复数计算：

import cmath
print('π =', cmath.pi)
print('e =', cmath.e)
print('tau =', cmath.tau)
print('Positive infinity =', cmath.inf)
print('Positive Complex infinity =', cmath.infj)
print('NaN =', cmath.nan)
print('NaN Complex =', cmath.nanj)

结果

π = 3.141592653589793
e = 2.718281828459045
tau = 6.283185307179586
Positive infinity = inf
Positive Complex infinity = infj
NaN = nan
NaN Complex = nanj

电源和对数功能

该cmath()模块为对数和幂运算提供了一些有用的功能：

import cmath
c = 1 + 2j
print('e^c =', cmath.exp(c))
print('log2(c) =', cmath.log(c, 2))
print('log10(c) =', cmath.log10(c))
print('sqrt(c) =', cmath.sqrt(c))

结果

e^c = (-1.1312043837568135+2.4717266720048188j)
log2(c) = (1.1609640474436813+1.5972779646881088j)
log10(c) = (0.3494850021680094+0.480828578784234j)
sqrt(c) = (1.272019649514069+0.7861513777574233j)

三角函数

import cmath
c = 2 + 4j
print('arc sine value:\n ', cmath.asin(c))
print('arc cosine value :\n', cmath.acos(c))
print('arc tangent value of complex number c :\n', cmath.atan(c))
print('sine value:\n', cmath.sin(c))
print('cosine value:\n', cmath.cos(c))
print('tangent value:\n', cmath.tan(c))

结果

arc sine value:
(0.4538702099631225+2.198573027920936j)
arc cosine value :
(1.1169261168317741-2.198573027920936j)
arc tangent value of complex number c :
(1.4670482135772953+0.20058661813123432j)
sine value:
(24.83130584894638-11.356612711218174j)
cosine value:
(-11.36423470640106-24.814651485634187j)
tangent value:
(-0.0005079806234700387+1.0004385132020523j)

双曲函数

import cmath
c = 2 + 4j
print('Inverse hyperbolic sine value: \n', cmath.asinh(c))
print('Inverse hyperbolic cosine value: \n', cmath.acosh(c))
print('Inverse hyperbolic tangent value: \n', cmath.atanh(c))
print('Hyperbolic sine value: \n', cmath.sinh(c))
print('Hyperbolic cosine value: \n', cmath.cosh(c))
print('Hyperbolic tangent value: \n', cmath.tanh(c))

结果

Inverse hyperbolic sine value:
(2.183585216564564+1.096921548830143j)
Inverse hyperbolic cosine value:
(2.198573027920936+1.1169261168317741j)
Inverse hyperbolic tangent value:
(0.09641562020299617+1.3715351039616865j)
Hyperbolic sine value:
(-2.370674169352002-2.8472390868488278j)
Hyperbolic cosine value:
(-2.4591352139173837-2.744817006792154j)
Hyperbolic tangent value:
(1.0046823121902348+0.03642336924740368j)