Python complex get real

cmath — Mathematical functions for complex numbers¶

This module provides access to mathematical functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments. They will 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.

For functions involving branch cuts, we have the problem of deciding how to define those functions on the cut itself. Following Kahan’s “Branch cuts for complex elementary functions” paper, as well as Annex G of C99 and later C standards, we use the sign of zero to distinguish one side of the branch cut from the other: for a branch cut along (a portion of) the real axis we look at the sign of the imaginary part, while for a branch cut along the imaginary axis we look at the sign of the real part.

For example, the cmath.sqrt() function has a branch cut along the negative real axis. An argument of complex(-2.0, -0.0) is treated as though it lies below the branch cut, and so gives a result on the negative imaginary axis:

>>> cmath.sqrt(complex(-2.0, -0.0)) -1.4142135623730951j 

But an argument of complex(-2.0, 0.0) is treated as though it lies above the branch cut:

>>> cmath.sqrt(complex(-2.0, 0.0)) 1.4142135623730951j 

Conversions to and from polar coordinates¶

A Python complex number z is stored internally using rectangular or Cartesian coordinates. It is completely determined by its real part z.real and its imaginary part z.imag . In other words:

Polar coordinates give an alternative way to represent a complex number. In polar coordinates, a complex number z is defined by the modulus r and the phase angle phi. The modulus r is the distance from z to the origin, while the phase phi is the counterclockwise angle, measured in radians, from the positive x-axis to the line segment that joins the origin to z.

The following functions can be used to convert from the native rectangular coordinates to polar coordinates and back.

Return the phase of x (also known as the argument of x), as a float. phase(x) is equivalent to math.atan2(x.imag, x.real) . The result lies in the range [-π, π], and the branch cut for this operation lies along the negative real axis. The sign of the result is the same as the sign of x.imag , even when x.imag is zero:

>>> phase(complex(-1.0, 0.0)) 3.141592653589793 >>> phase(complex(-1.0, -0.0)) -3.141592653589793 

The modulus (absolute value) of a complex number x can be computed using the built-in abs() function. There is no separate cmath module function for this operation.

Return the representation of x in polar coordinates. Returns a pair (r, phi) where r is the modulus of x and phi is the phase of x. polar(x) is equivalent to (abs(x), phase(x)) .

Return the complex number x with polar coordinates r and phi. Equivalent to r * (math.cos(phi) + math.sin(phi)*1j) .

Power and logarithmic functions¶

Return e raised to the power x, where e is the base of natural logarithms.

Returns the logarithm of x to the given base. If the base is not specified, returns the natural logarithm of x. There is one branch cut, from 0 along the negative real axis to -∞.

Return the base-10 logarithm of x. This has the same branch cut as log() .

Return the square root of x. This has the same branch cut as log() .

Trigonometric functions¶

Return the arc cosine of x. There are two branch cuts: One extends right from 1 along the real axis to ∞. The other extends left from -1 along the real axis to -∞.

Return the arc sine of x. This has the same branch cuts as acos() .

Return the arc tangent of x. There are two branch cuts: One extends from 1j along the imaginary axis to ∞j . The other extends from -1j along the imaginary axis to -∞j .

Hyperbolic functions¶

Return the inverse hyperbolic cosine of x. There is one branch cut, extending left from 1 along the real axis to -∞.

Return the inverse hyperbolic sine of x. There are two branch cuts: One extends from 1j along the imaginary axis to ∞j . The other extends from -1j along the imaginary axis to -∞j .

Return the inverse hyperbolic tangent of x. There are two branch cuts: One extends from 1 along the real axis to ∞ . The other extends from -1 along the real axis to -∞ .

Return the hyperbolic cosine of x.

Return the hyperbolic sine of x.

Return the hyperbolic tangent of x.

Classification functions¶

Return True if both the real and imaginary parts of x are finite, and False otherwise.

Return True if either the real or the imaginary part of x is an infinity, and False otherwise.

Return True if either the real or the imaginary part of x is a NaN, and False otherwise.

Return True if the values a and b are close to each other and False otherwise.

Whether or not two values are considered close is determined according to given absolute and relative tolerances.

rel_tol is the relative tolerance – it is the maximum allowed difference between a and b, relative to the larger absolute value of a or b. For example, to set a tolerance of 5%, pass rel_tol=0.05 . The default tolerance is 1e-09 , which assures that the two values are the same within about 9 decimal digits. rel_tol must be greater than zero.

abs_tol is the minimum absolute tolerance – useful for comparisons near zero. abs_tol must be at least zero.

The IEEE 754 special values of NaN , inf , and -inf will be handled according to IEEE rules. Specifically, NaN is not considered close to any other value, including NaN . inf and -inf are only considered close to themselves.

PEP 485 – A function for testing approximate equality

Constants¶

The mathematical constant π, as a float.

The mathematical constant e, as a float.

The mathematical constant τ, as a float.

Floating-point positive infinity. Equivalent to float(‘inf’) .

Complex number with zero real part and positive infinity imaginary part. Equivalent to complex(0.0, float(‘inf’)) .

A floating-point “not a number” (NaN) value. Equivalent to float(‘nan’) .

Complex number with zero real part and NaN imaginary part. Equivalent to complex(0.0, float(‘nan’)) .

Note that the selection of functions is similar, but not identical, to that in module math . The reason for having two modules is that some users aren’t interested in complex numbers, and perhaps don’t even know what they are. They would rather have math.sqrt(-1) raise an exception than return a complex number. Also note that the functions defined in cmath always return a complex number, even if the answer can be expressed as a real number (in which case the complex number has an imaginary part of zero).

A note on branch cuts: They are curves along which the given function fails to be continuous. They are a necessary feature of many complex functions. It is assumed that if you need to compute with complex functions, you will understand about branch cuts. Consult almost any (not too elementary) book on complex variables for enlightenment. For information of the proper choice of branch cuts for numerical purposes, a good reference should be the following:

Kahan, W: Branch cuts for complex elementary functions; or, Much ado about nothing’s sign bit. In Iserles, A., and Powell, M. (eds.), The state of the art in numerical analysis. Clarendon Press (1987) pp165–211.

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Complex Numbers in Python

In this Python Tutorial, we will learn about Complex Numbers in Python. In addition, we will learn how to input complex numbers in Python with different examples.

Introduction to Complex Numbers

Before delving into the Python aspect, let’s take a moment to understand what complex numbers are.

A complex number is a number that can be expressed in the form a + bi, where ‘a’ and ‘b’ are real numbers, and ‘i’ is the imaginary unit with the property i² = -1. ‘a’ is referred to as the real part, while ‘b’ is the imaginary part of the complex number.

Creating Complex Numbers in Python

Python provides two ways to define a complex number:

1.The first method involves directly assigning the real and imaginary parts with the j notation:

# Defining a complex number z = 3 + 4j print(z) 

2.The second method involves using the built-in complex() function, which accepts the real and imaginary parts as arguments and returns a complex number:

# Using the complex() function to define a complex number z = complex(3, 4) print(z)

Accessing Attributes of Complex Numbers in Python

Python provides two attributes, real and imag , for a complex number object, which returns the real and imaginary parts of the complex number, respectively.

# Creating a complex number z = 3 + 4j # Printing the real and imaginary parts print(z.real) print(z.imag) 

Input Complex Number in Python

You can input a complex number in Python by using the input() function and then converting the input to a complex number using the complex() function.

Here’s a simple Python program that prompts the user to input a complex number:

# Program to input a complex number # Prompt user for real part of the complex number real_part = float(input("Enter the real part: ")) # Prompt user for imaginary part of the complex number imaginary_part = float(input("Enter the imaginary part: ")) # Form the complex number z = complex(real_part, imaginary_part) # Print the complex number print("The complex number is: ", z) 

This program prompts the user to enter the real and imaginary parts separately. The input() function returns a string, so we use the float() function to convert the inputs to floating-point numbers. The complex() function then takes these two numbers and forms a complex number.

You can also get the complex number as a string and then convert it to a complex number. Here’s how:

# Program to input a complex number as a string # Prompt user for the complex number as a string z_string = input("Enter a complex number in the form a+bj: ") # Convert the string to a complex number z = complex(z_string) # Print the complex number print("The complex number is: ", z) 

In this program, the user must input the complex number in the form a+bj or a-bj , where a is the real part and b is the imaginary part. Again, you should add error handling to make this program robust.

Conclusion

Python natively supports complex numbers, which are crucial for many mathematical computations. Complex numbers can be defined directly using a + bj syntax or using the complex() function. Python allows access to real and imaginary parts through the .real and .imag attributes respectively.

You may also like to read the following Python tutorials.

I am Bijay Kumar, a Microsoft MVP in SharePoint. Apart from SharePoint, I started working on Python, Machine learning, and artificial intelligence for the last 5 years. During this time I got expertise in various Python libraries also like Tkinter, Pandas, NumPy, Turtle, Django, Matplotlib, Tensorflow, Scipy, Scikit-Learn, etc… for various clients in the United States, Canada, the United Kingdom, Australia, New Zealand, etc. Check out my profile.

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