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The Python has a cmath module which contains number of mathematical functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments. It also accept any Python object that has either a __complex__() or a __float__() method: these methods are used to convert the object to a complex or floating-point number, respectively, and the function is then applied to the result of the conversion.

The functions and constants of cmath module are listed below:

Python cmath Functions

MethodDescription
phase() Return the argument of a complex number.
polar() Return the representation of a complex number in polar coordinates.
rect() Convert a complex number from polar coordinates to rectangular coordinates.
isclose() Check if two values are close to each other.
isfinite() Check if the argument is neither an infinity nor a NaN.
isinf() Check if the argument is positive or negative infinity.
isnan() Check if the argument is a NaN (not a number).

Power & Logarithmic Functions

FunctionsDescription
exp() Returns the exponent of e.
log() Returns the logarithm of a given number to the given base.
log10() Returns the base-10 logarithm of a given complex number.
sqrt() Returns the square root of the given complex number.

Trigonometric Functions

FunctionsDescription
sin() Returns the complex sine of a complex number.
cos() Returns the complex cosine of a complex number.
tan() Returns the complex tangent of a complex number.
asin() Returns the complex arc sine of a complex number.
acos() Returns the complex arc cosine of a complex number.
atan() Returns the complex arc tangent of a complex number.

Hyperbolic Functions

FunctionsDescription
sinh() Returns the complex hyperbolic sine of a complex number.
cosh() Returns the complex hyperbolic cosine of a complex number.
tanh() Returns the complex hyperbolic tangent of a complex number.
asinh() Returns the complex inverse hyperbolic sine of a complex number.
acosh() Returns the complex inverse hyperbolic cosine of a complex number.
atanh() Returns the complex inverse hyperbolic tangent of a complex number.

Constants

FunctionsDescription
pi Returns the value of 𝜋 to the available precision.
e Returns the value of e to the available precision.
tau Returns the value of Τ to the available precision.
inf Returns a floating-point positive infinity.
infj Returns a complex number with zero real part and positive infinity imaginary part.
nan Returns a floating-point "not a number" (NaN) value.
nanj Returns a complex number with zero real part and NaN imaginary part.

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