A complex number has two parts, real part and imaginary part. Complex numbers are represented as A+Bi or A+Bj, where A is real part and B is imaginary part. First thing first, python uses We can create complex number from two real numbers. Syntax for doing this is: Where, a & b are of real data types and c will be of complex data types.
Let's try it out in python console: After creating complex data type, we can access real and imaginary part using built-in data descriptors We can read complex number directly from user using built-in function Output Complex data type has built-in method called Python supports direct addition, subtraction, multiplication and division using operator Python supports complex data type as built-in feature which means we can directly perform different operations on complex
number in python.
A+Bj notation to represent complex number meaning python will recognize 3+4j as a valid number but 3+4i is not valid. Let's try it out in python console:
>>> a=3+4j
>>> b=3+4i
SyntaxError: invalid syntax
Creating Complex Data Type Using complex[]
c = complex[a,b]
>>> a=5
>>> b=7
>>> c=complex[a,b]
>>> print[c]
[5+7j]
Accessing Real and Imaginary Part From Complex Number
real and imag. Let's try it out in python console:
>>> a = 5+6j
>>> a.real
5.0
>>> a.imag
6.0
Reading Complex Number From User
input[]. Since function input[] returns STRING we must convert result to
complex using function complex[]. Try following example:
a = complex[input['Enter complex number:']]
print['Given complex number is:',a]
Enter complex number:2+3j
Given complex number is: [2+3j]
Finding Conjugate of Complex Number
conjugate[] to find conjugate of complex number. Let's try it out in python console:
>>> a=10-6j
>>> a.conjugate[]
[10+6j]
Addition, Subtraction, Multiplication & Division on Complex Number
+, -, *, /. Let's
try it out in python console:
>>> a=1+2j
>>> b=3+4j
>>> a+b
[4+6j]
>>> a-b
[-2-2j]
>>> a*b
[-5+10j]
>>> a/b
[0.44+0.08j]
Data types in Python
Every value in Python has a datatype. Since everything is an object in Python programming, data types are actually classes and variables are instance [object] of these classes.
There are various data types in Python. Some of the important types are listed below.
Python Numbers
Integers, floating point numbers and complex numbers fall under
Python numbers category. They are defined as int, float and complex classes in Python.
We can use the type[] function to know which class a variable or a value belongs to. Similarly, the isinstance[] function is used to check if an object belongs to a particular class.
a = 5
print[a, "is of type", type[a]]
a = 2.0
print[a, "is of type", type[a]]
a = 1+2j
print[a, "is complex number?", isinstance[1+2j,complex]]
Output
5 is of type 2.0 is of type [1+2j] is complex number? True
Integers can be of any length, it is only limited by the memory available.
A floating-point number is accurate up to 15 decimal places. Integer and floating points are separated by decimal points. 1 is an integer, 1.0 is a floating-point number.
Complex numbers are written in the form, x + yj, where x is the real part and y is the imaginary part. Here are some examples.
>>> a = 1234567890123456789
>>> a
1234567890123456789
>>> b = 0.1234567890123456789
>>> b
0.12345678901234568
>>> c = 1+2j
>>> c
[1+2j]
Notice that the float variable b got truncated.
Python List
List is an ordered sequence of items. It is one of the most used datatype in Python and is very flexible. All the items in a list do not need to be of the same type.
Declaring a list is pretty straight forward. Items separated by commas are enclosed within brackets [ ].
a = [1, 2.2, 'python']
We can use the slicing operator [ ] to extract an item or a range of items from a list. The index starts from 0 in
Python.
a = [5,10,15,20,25,30,35,40]
# a[2] = 15
print["a[2] = ", a[2]]
# a[0:3] = [5, 10, 15]
print["a[0:3] = ", a[0:3]]
# a[5:] = [30, 35, 40]
print["a[5:] = ", a[5:]]
Output
a[2] = 15 a[0:3] = [5, 10, 15] a[5:] = [30, 35, 40]
Lists are mutable, meaning, the value of elements of a list can be altered.
a = [1, 2, 3]
a[2] = 4
print[a]
Output
[1, 2, 4]
Python Tuple
Tuple is an ordered sequence of items same as a list. The only difference is that tuples are immutable. Tuples once created cannot be modified.
Tuples are used to write-protect data and are usually faster than lists as they cannot change dynamically.
It is defined within parentheses [] where items are separated by commas.
t = [5,'program', 1+3j]
We can use the slicing operator [] to extract items but we cannot change its value.
t = [5,'program', 1+3j]
# t[1] = 'program'
print["t[1] = ", t[1]]
# t[0:3] = [5, 'program', [1+3j]]
print["t[0:3] = ", t[0:3]]
# Generates error
# Tuples are immutable
t[0] = 10
Output
t[1] = program
t[0:3] = [5, 'program', [1+3j]]
Traceback [most recent call last]:
File "test.py", line 11, in
t[0] = 10
TypeError: 'tuple' object does not support item assignment
Python Strings
String is sequence of Unicode characters. We can use single quotes or double quotes to
represent strings. Multi-line strings can be denoted using triple quotes, ''' or """.
s = "This is a string"
print[s]
s = '''A multiline
string'''
print[s]
Output
This is a string A multiline string
Just like a list and tuple, the slicing operator [ ] can be used with strings. Strings, however, are immutable.
s = 'Hello world!'
# s[4] = 'o'
print["s[4] = ", s[4]]
# s[6:11] = 'world'
print["s[6:11] = ", s[6:11]]
# Generates error
# Strings are immutable in Python
s[5] ='d'
Output
s[4] = o s[6:11] = world Traceback [most recent call last]: File "", line 11, in TypeError: 'str' object does not support item assignment
Python Set
Set is an unordered collection of unique items. Set is defined by values
separated by comma inside braces { }. Items in a set are not ordered.
a = {5,2,3,1,4}
# printing set variable
print["a = ", a]
# data type of variable a
print[type[a]]
Output
a = {1, 2, 3, 4, 5}
We can perform set operations like union, intersection on two sets. Sets have unique values. They eliminate duplicates.
a = {1,2,2,3,3,3}
print[a]
Output
{1, 2, 3}
Since, set are unordered collection, indexing has no meaning. Hence, the slicing operator [] does not work.
>>> a = {1,2,3}
>>> a[1]
Traceback [most recent call last]:
File "", line 301, in runcode
File "", line 1, in
TypeError: 'set' object does not support indexing
Python Dictionary
Dictionary is an unordered collection of key-value pairs.
It is generally used when we have a huge amount of data. Dictionaries are optimized for retrieving data. We must know the key to retrieve the value.
In Python, dictionaries are defined within braces {} with each item being a pair in the form key:value. Key and value can be of any type.
>>> d = {1:'value','key':2}
>>> type[d]
We use key to retrieve the respective value. But not the other way around.
d = {1:'value','key':2}
print[type[d]]
print["d[1] = ", d[1]]
print["d['key'] = ", d['key']]
# Generates error
print["d[2] = ", d[2]]
Output
d[1] = value d['key'] = 2 Traceback [most recent call last]: File "", line 9, in KeyError: 2
Conversion between data types
We can convert between different data types by using different type conversion functions like int[], float[], str[], etc.
>>> float[5]
5.0
Conversion from float to int will truncate the value [make it closer to zero].
>>> int[10.6]
10
>>> int[-10.6]
-10
Conversion to and from string must contain compatible values.
>>> float['2.5']
2.5
>>> str[25]
'25'
>>> int['1p']
Traceback [most recent call last]:
File "", line 301, in runcode
File "", line 1, in
ValueError: invalid literal for int[] with base 10: '1p'
We can even convert one sequence to another.
>>> set[[1,2,3]]
{1, 2, 3}
>>> tuple[{5,6,7}]
[5, 6, 7]
>>> list['hello']
['h', 'e', 'l', 'l', 'o']
To convert to dictionary, each element must be a pair:
>>> dict[[[1,2],[3,4]]]
{1: 2, 3: 4}
>>> dict[[[3,26],[4,44]]]
{3: 26, 4: 44}