Complex Data Type

Understanding Complex Numbers

In Python, the complex data type represents complex numbers. A complex number is a number that can be expressed in the form a + bj, where:

• a is the real part

• b is the imaginary part

• j is the imaginary unit, defined as the square root of -1

Creating Complex Numbers

To create a complex number, you can use the following syntax:

Python

z = complex(real, imag)

where real and imag are the real and imaginary parts, respectively.

Alternatively, you can use the j suffix:

Python

z = 3 + 2j

Example

Python

# Creating complex numbers

z1 = complex(3, 2)

z2 = 4 - 5j

print(z1)  # Output: (3+2j)

print(z2)  # Output: (4-5j)

Accessing Real and Imaginary Parts

You can access the real and imaginary parts of a complex number using the real and imag attributes:

Python

z = 3 + 2j

real_part = z.real

imag_part = z.imag

print(real_part)  # Output: 3.0

print(imag_part)  # Output: 2.0

Complex Arithmetic

Python supports arithmetic operations on complex numbers:

Python

z1 = 3 + 2j

z2 = 1 - 4j

sum_complex = z1 + z2

difference = z1 - z2

product = z1 * z2

quotient = z1 / z2

print(sum_complex)  # Output: (4-2j)

print(difference)  # Output: (2+6j)

print(product)  # Output: (19+10j)

print(quotient)  # Output: (-0.2-0.8j)

Built-in Functions

While there are no specific methods for the complex data type, Python provides some built-in functions that can be used with complex numbers:

• abs(z): Returns the magnitude (absolute value) of the complex number z.

• conjugate(z): Returns the complex conjugate of z.

Example

Python

z = 3 + 4j

magnitude = abs(z)

conjugate = z.conjugate()

print(magnitude)  # Output: 5.0

print(conjugate)  # Output: (3-4j)

Complex numbers are essential in various fields, including mathematics, physics, and engineering. Python's support for complex numbers makes it a versatile language for these domains.