complex — Complex Number Data Type

Visual reference

What you will learn

• Complex notation — a + bj and a - bj
• Real and imaginary — access with .real and .imag
• Pure imaginary numbers — values like 5j
• Common mistakes — why i is invalid in Python

Big picture: what is a complex number?

So far in the fundamental types:

Type	Example	Role
int	5	Whole numbers
float	3.14	Decimal numbers
bool	True	Logical values
complex	2 + 3j	Real + imaginary parts

A complex number has two parts:

Together they form 2 + 3j.

complex is a pre-defined class and a fundamental type. Purpose: store complex data in the form a + bj or a - bj.

Why does Python use j instead of i?

In mathematics, the imaginary unit is often written i, where i² = −1.

In Python (and much of engineering), the imaginary unit is j, where j² = −1.

Reason: in electrical engineering, i often means electric current, so j avoids confusion.

Valid	Invalid
3j, 2 + 3j	3i, 10 + 2i

# z = 3i
# SyntaxError: invalid decimal literal

General form

Every complex number follows:

a + bj

Symbol	Meaning	Example
a	Real part	2
b	Imaginary coefficient	3
j	Imaginary unit (√−1)	attached to b

a = 2 + 3j
b = -2 - 3j
c = 10 + 2.5j
d = 2.3 + 4.6j

print(a)
print(b)
print(c)
print(d)

(2+3j)
(-2-3j)
(10+2.5j)
(2.3+4.6j)

Python prints complex values in parentheses.

Pure imaginary numbers

A complex number does not need a visible real part. 0 + 5j can be written as 5j.

x = 5j
y = -2.3j

print(x)
print(y)

5j
(-0-2.3j)

Why -0? The real part is 0.0 and the imaginary coefficient is negative — Python’s display shows (-0-2.3j) (your notes mark this as important).

Accessing real and imaginary parts

Use two built-in attributes (from your notes):

Attribute	Returns
.real	Real component
.imag	Imaginary component

z = 2 + 3j

print(z.real)
print(z.imag)

2.0
3.0

Important observation

You may write integers (2 and 3), but .real and .imag return floats. Internally, both parts are treated as float type.

print(type(z.real), type(z.imag))

<class 'float'> <class 'float'>

Interactive: build your own complex number

In the playground below, change z = 2 + 3j to any a + bj, run, and inspect .real and .imag. Try (2 + 3j) + (1 + 1j) to get (3+4j).

Imaginary-only example

z = 3.4j

print(z.real)
print(z.imag)

0.0
3.4

The value lies on the imaginary axis; real part is 0.0.

From your notes:

a = -3.5j
print(a.real, a.imag)

-0.0 -3.5

Common mistakes

Mistake 1 — using i:

# z = 5i
# SyntaxError: invalid decimal literal

Mistake 2 — using .imaginary:

z = 2 + 3j
# z.imaginary
# AttributeError: 'complex' object has no attribute 'imaginary'

Correct:

z = 5j
print(z.imag)

Where are complex numbers used?

Beginners use them less often, but they are essential in many fields.

Electrical engineering — AC circuits and impedance

Signal processing — Fourier transform

Quantum physics — wave functions

Medical imaging — MRI and reconstruction

Practice exercises

Exercise 1 — create z = 1 - 1j and print parts:

z = 1 - 1j
print(z.real)
print(z.imag)

1.0
-1.0

Exercise 2 — add two complex numbers:

a = 2 + 3j
b = 1 + 1j
print(a + b)

(3+4j)

Exercise 3 — why does 5j have real == 0.0?

Because 5j is 0 + 5j. The real component exists; it is 0.0.

Quick knowledge check

1. Imaginary unit in Python?
   j, not i.

2. Attributes for components?
   .real and .imag.

3. Type of z.real for 2 + 3j?
   float (2.0).

Summary

• complex stores numbers with real and imaginary parts: a + bj.
• Python uses j (engineering convention), not i.
• Read parts with .real and .imag (both return float).
• 5j is valid; real part is 0.0.
• Used in EE, signal processing, physics, and scientific computing.

Next lesson: str — string data type (text, quotes, and operations).