Complex Numbers in Python

In Python, complex numbers are represented using the form a + bj, where a and b are real numbers, and j is the imaginary unit (√-1).

Complex numbers in Python can be declared using the complex() function or directly using the notation a + bj:

complex_number1 = complex(1, 2)
print(complex_number1)  # Output: (1+2j)

complex_number2 = 3 + 4j
print(complex_number2)  # Output: (3+4j)

It is possible to access the real and imaginary parts of a complex number using the attributes .real and .imag, respectively:

number = 1 + 2j
real_part = number.real
imaginary_part = number.imag
print(real_part, imaginary_part)  # Output: 1.0 2.0

Python uses the standard representation of complex numbers according to the IEEE 754 standard for double-precision floating-point numbers.

Operations with complex numbers

Python supports several mathematical operations with complex numbers, including addition, subtraction, multiplication, division, and other specific operations for complex numbers.

Basic operations behave as expected for complex numbers:

# Addition
sum_result = (1 + 2j) + (3 + 4j)
print(sum_result)  # Output: (4+6j)

# Subtraction
subtraction = (5 + 6j) - (2 + 1j)
print(subtraction)  # Output: (3+5j)

# Multiplication
multiplication = (2 + 3j) * (4 + 5j)
print(multiplication)  # Output: (-7+22j)

# Division
division = (5 + 6j) / (2 + 1j)
print(division)  # Output: (4+1j)

Python also provides functions and methods for working with complex numbers, such as the conjugate (conjugate()), magnitude (abs()), and argument (phase()):

# Conjugate
number = 3 + 4j
conjugate = number.conjugate()
print(conjugate)  # Output: (3-4j)

# Magnitude
magnitude = abs(number)
print(magnitude)  # Output: 5.0 (square root of 3^2 + 4^2)

# Argument (phase)
argument = cmath.phase(number)
print(argument)  # Output: 0.9272952180016122 (in radians)

Conversion between types

It is possible to convert other data types to complex numbers using the complex() function:

# Conversion from integers
integer_number = 5
complex_number = complex(integer_number)
print(complex_number)  # Output: (5+0j)

# Conversion from floats
float_number = 3.14
complex_number = complex(float_number)
print(complex_number)  # Output: (3.14+0j)