Python number operations (3) cmath module

The cmath module provides related mathematical operation functions for complex numbers, so that complex numbers can be calculated like integer or floating-point numbers.

Complex Polar Coordinate System Conversion Function

In the Python data type (1) number type , we talked about the storage essence of complex numbers and the definition in the polar coordinate system. The relevant polar coordinate conversion functions are as follows:

Function name	Paraphrase
cmath.phase(x)	Returns the radians of x as a floating point number, in the range of [-π, π]
cmath.polar(x)	Returns the coordinate of x in the polar coordinate system (r, phi)
cmath.rect(r, phi)	Returns the complex number corresponding to the coordinates (r, phi) in the polar coordinate system

>>> import cmath
>>> cmath.phase(complex(-1.0, 0.0))
3.141592653589793
>>> cmath.phase(complex(-1.0,0.0))
3.141592653589793
>>> cmath.phase(complex(-0.5, 0.0))
3.141592653589793
>>> cmath.phase(complex(-0.5, 0.3))
2.601173153319209
>>> cmath.polar(complex(-0.5, 0.3))
(0.58309518948453, 2.601173153319209)
>>> cmath.rect(0.58309518948453, 2.601173153319209)
(-0.49999999999999994+0.3j)

Power function and logarithmic function

function	Paraphrase
cmath.exp(x)	return`e**x`
cmath.log(x,base)	Returns the logarithm of x with base as the base
cmath.log10(x)	Returns the base 10 logarithm of x
cmath.sqrt(x)	square root of x

>>> cmath.exp(complex(2.0, 0.0))
(7.38905609893065+0j)
>>> cmath.exp(complex(10.0, 2.0))
(-9166.244060822655+20028.608669281643j)
>>> cmath.log10(complex(100.0,2.0))
(2.0000868415292326+0.008684731797315706j)
>>> cmath.sqrt(complex(2.0, 1.0))
(1.455346690225355+0.34356074972251244j)

Trigonometric function

function	Paraphrase
cmath.acos(x)	Returns the arc cosine of x
cmath.asin(x)	Returns the arc sine of x
cmath.atan(x)	Returns the arctangent of x
cmath.cos(x)	Returns the cosine of x
cmath. sin (x)	Returns the sine of x
cmath.tan(x)	Returns the tangent of x

Hyperbolic function

function	Paraphrase
cmath.acosh(x)	Returns the arc cosine of x in the hyperbola
cmath.asinh(x)	Returns the arc sine of x in the hyperbola
cmath.atanh(x)	Returns the arctangent of x in the hyperbola
cmath.cosh(x)	Returns the cosine of x in the hyperbola
cmath. birth (x)	Returns the sine of x in the hyperbola
cmath. fishy (x)	Returns the tangent of x in the hyperbola

Classification function

function	Paraphrase
cmath.isfinite(x)	If the modulus r and the radian phi are both rational numbers, it returns True, otherwise it returns False
cmath.isinf(x)	If the modulus r and the radian phi are both close to positive infinity, it returns True, otherwise it returns False
cmath.isnan(x)	If the modulus r and the radian phi are both Nan, it returns True, otherwise it returns False
cmath.isclose(a,b,*,rel_tol,abs_tol)	If the values of a and b are relatively close, it returns True, otherwise it returns False. The criterion is based on the given absolute and relative tolerances. rel_tol is the relative tolerance, must be greater than 0, is the maximum allowable difference between a and b. abs_tol is the minimum absolute tolerance, at least 0

constant

Constant name	Paraphrase
cmath.pi	The constant π=3.141926...
cmath.e	The constant e= 2.718281...
cmath. your	The constant τ = 6.283185..., which is twice π
cmath.inf	Positive infinity floating point number
cmath.infj	The real part is 0 and the imaginary part is a complex number with positive infinity floating point numbers
cmath. in	Floating point number "not a number"
cmath. nanj	The real part is 0, and the imaginary part is the "non-numeric value" of Nan

Many functions of cmath module and math module look similar, but they are actually different functions. The value returned by cmath is a complex number, even if the imaginary part is 0. Many people do not understand why a cmath module is defined separately instead of a math module to solve complex number arithmetic problems together. Suppose one day you need to use a particularly complicated way to calculate, you will understand the reason for such a definition.