1. What is a Complex Data Type?

In Python, a complex number is a built-in data type that is specifically used for mathematical and scientific computations. A complex number consists of a real part and an imaginary part, just like in algebra.

Don’t be misled by the word “complex” — it refers to the mathematical concept, not the difficulty level.

Python supports complex numbers natively, unlike many other programming languages such as C, C++, or Java.

2. Mathematical Background

A complex number is generally written in the form:

a + bj

Where:

• a is the real part
• b is the imaginary part
• j is the imaginary unit, where j² = -1

In Python, the imaginary unit must be represented with the letter j or J. Using i (as in traditional mathematics) will cause a syntax error.

3. Syntax in Python

x = 10 + 20j

• This defines x as a complex number.
• Python understands both lowercase j and uppercase J.

3.1 Invalid Example

x = 10 + 20i  # This will raise a SyntaxError

4. Verifying the Data Type

x = 10 + 20j
print(type(x))  # Output: <class 'complex'>

5. Accessing Real and Imaginary Parts

You can use .real and .imag attributes to access parts of a complex number.

x = 10 + 20j
print(x.real)  # Output: 10.0
print(x.imag)  # Output: 20.0

Note: Even if you define integers, Python returns the parts as float values.

6. Accepted Value Types

Both the real and imaginary parts can be either integers or floating-point numbers:

x = 10.5 + 20.6j  # Valid
x = 0b1111 + 20j  # Binary for real part, valid

The imaginary part must be in decimal. You cannot use binary, octal, or hexadecimal for it.

x = 15 + 0b1111j  # ❌ Invalid: SyntaxError

7. Arithmetic Operations with Complex Numbers

Python allows you to perform arithmetic operations directly with complex numbers:

x = 10 + 20j
y = 20 + 30j

print(x + y)   # Output: (30+50j)
print(x - y)   # Output: (-10-10j)
print(x * y)   # Output: (-400+700j)
print(x / y)   # Output: (0.7307692307692307+0.038461538461538464j)

8. When to Use Complex Numbers in Python

You’ll typically use complex numbers in:

• Scientific computing
• Electrical engineering simulations
• Signal processing
• Mathematics-heavy applications

For everyday programming, you may rarely use them.

9. Common Mistakes

Mistake	Fix
Using i instead of j	Use j or J only
Using binary/octal in imaginary part	Use only decimal
Expecting real/imag parts as int	They’re returned as float