In Python, a complex data type represents numbers in the form of a + bj, where ‘a’ and ‘b’ are real numbers and ‘j’ is the imaginary unit. The complex data type is useful when dealing with mathematical operations involving complex numbers. In this tutorial, we will explore the concept of complex data types in Python with examples.

To create a complex number in Python, we can use the built-in `complex()` function. Let’s consider an example:

**Example 1:**

“`python

z = complex(2, 3)

print(z)

“`

In this example, we create a complex number `z` with a real part of 2 and an imaginary part of 3. The output will be `(2+3j)`, indicating that it is a complex number.

__Basic Operations on Complex Numbers:__

Python provides various operations that can be performed on complex numbers. Let’s explore some of these operations:

**Addition:**

To add two complex numbers, we can simply use the `+` operator. The real and imaginary parts of both numbers will be added separately.

**Example 2:**

“`python

z1 = complex(2, 3)

z2 = complex(4, 5)

result = z1 + z2

print(result)

“`

The output will be `(6+8j)`, indicating that the sum of `z1` and `z2` is `(6+8j)`.

**Subtraction:**

To subtract one complex number from another, we can use the `-` operator. Similar to addition, subtraction is performed on the real and imaginary parts separately.

**Example 3:**

“`python

z1 = complex(2, 3)

z2 = complex(4, 5)

result = z1 – z2

print(result)

“`

The output will be `(-2-2j)`, indicating that the difference between `z1` and `z2` is `(-2-2j)`.

**Multiplication:**

To multiply two complex numbers, we can use the `*` operator. The multiplication is performed using the rules of complex arithmetic.

**Example 4:**

“`python

z1 = complex(2, 3)

z2 = complex(4, 5)

result = z1 * z2

print(result)

“`

The output will be `(-7+22j)`, indicating that the product of `z1` and `z2` is `(-7+22j)`.

**Division:**

To divide one complex number by another, we can use the `/` operator. The division is performed using the rules of complex arithmetic.

**Example 5:**

“`python

z1 = complex(2, 3)

z2 = complex(4, 5)

result = z1 / z2

print(result)

“`

The output will be `(0.5609756097560976+0.0487804878048781j)`, indicating that the quotient of `z1` and `z2` is `(0.0487804878048781j)`.

__Accessing Real and Imaginary Parts:__

We can access the real and imaginary parts of a complex number using the `.real` and `.imag` attributes respectively. Let’s consider an example:

**Example 6:**

“`python

z = complex(2, 3)

print(z.real) # Output: 2.0

print(z.imag) # Output: 3.0

“`

In this example, we create a complex number `z` and print its real and imaginary parts using the `.

__Conclusion:__

In Python, complex data types allow us to work with complex numbers efficiently. They provide various operations such as addition, subtraction, multiplication, and division. By utilizing the `.imag` attributes, we can access the real and imaginary parts of a complex number effortlessly.

Now that you have a better understanding of complex data types in Python, you can confidently incorporate them into your programs when dealing with complex mathematical operations.