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Python - complex Data Type

Introduction

The complex data type is used to represent complex numbers.

A complex number is written in the form a + bj.

  • a = Real Part
  • b = Imaginary Part
  • j = Imaginary Unit (√-1)

Structure of a Complex Number

Part Description
a Real Part
b Imaginary Part
j Imaginary Unit (√-1)

Examples of Complex Numbers

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main.py
Python 3 Runtime
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(3+5j)
(10+5.5j)
(0.5+0.1j)

Real Part of a Complex Number

The real part of a complex number can be represented using different number systems.

  • Decimal
  • Binary
  • Octal
  • Hexadecimal

Example

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main.py
Python 3 Runtime
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(3+5j)

Imaginary Part of a Complex Number

The imaginary part must always be written in decimal form.

Binary, octal, and hexadecimal values are not allowed in the imaginary part.

Invalid Example

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main.py
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SyntaxError

Arithmetic Operations on Complex Numbers

Python supports arithmetic operations on complex numbers.

Addition

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main.py
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(30+4j)

Subtraction

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main.py
Python 3 Runtime
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(10+3j)

Multiplication

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main.py
Python 3 Runtime
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(-4+7j)

Accessing Real and Imaginary Parts

Python provides two built-in attributes for complex numbers.

Attribute Purpose
real Returns the real part.
imag Returns the imaginary part.

Example

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main.py
Python 3 Runtime
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10.5
3.6

Checking the Data Type

The type() function returns the data type of a value.

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No output captured.

Important Mathematical Note

For complex numbers:

j² = -1

Applications of Complex Numbers

Complex numbers are commonly used in:

  • Scientific Applications
  • Electrical Engineering
  • Electronics
  • Signal Processing
  • Electrical Circuits
  • Mathematical Calculations

Difference Between int, float, and complex

Data Type Example Description
int 10 Whole numbers
float 10.5 Decimal numbers
complex 10+5j Complex numbers

Important Points

  • Complex numbers are immutable.
  • The real part supports decimal, binary, octal, and hexadecimal values.
  • The imaginary part supports only decimal values.
  • Python supports arithmetic operations on complex numbers.
  • Use real and imag to access different parts of a complex number.

Key Points

  • The complex data type represents complex numbers.
  • A complex number is written in the form a + bj.
  • The real part can use different number systems.
  • The imaginary part must always be in decimal form.
  • Use type() to check the data type.
  • Use real and imag to access the real and imaginary parts.

Quick Summary

Feature Description
Data Typecomplex
PurposeRepresents complex numbers
Formata + bj
Real PartSupports decimal, binary, octal, and hexadecimal
Imaginary PartDecimal only
Attributesreal, imag
MutableNo (Immutable)

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