Here’s a concise Python program to demonstrate each task listed:

### 1. Demonstrate various operators in Python:
“`python
# i) Arithmetic Operators
a, b = 10, 5
print(a + b, a – b, a * b, a / b, a % b, a ** b, a // b)

# ii) Relational Operators
print(a > b, a < b, a == b, a != b, a >= b, a <= b)

# iii) Assignment Operators
c = 10
c += 5
print(c)

# iv) Logical Operators
print(a > b and a != b, a > b or a < b, not a == b)

# v) Bitwise Operators
print(a & b, a | b, a ^ b, ~a, a << 1, a >> 1)

# vi) Ternary Operator
print(“Even” if a % 2 == 0 else “Odd”)

# vii) Membership Operators
lst = [1, 2, 3, 4, 5]
print(3 in lst, 6 not in lst)

# viii) Identity Operators
x = [1, 2]
y = [1, 2]
print(x is y, x is not y)
“`

### 2. Add and multiply complex numbers:
“`python
a = 3 + 4j
b = 1 + 2j
print(f”Sum: {a + b}, Product: {a * b}”)
“`

### 3. Find the length of a string without using libraries:
“`python
s = “Hello, World!”
length = 0
for char in s:
length += 1
print(length)
“`

### 4. Check if a substring is present in a string:
“`python
s = “Hello, World!”
sub = “World”
print(sub in s)
“`

### 5. Check if a key exists in a dictionary:
“`python
d = {‘name’: ‘Alice’, ‘age’: 25}
key = ‘age’
print(key in d)
“`

### 6. Add a new key-value pair to a dictionary:
“`python
d[‘city’] = ‘New York’
print(d)
“`

### 7. Operations on an array:
“`python
arr = [1, 2, 3, 4]
arr.append(5)
arr.insert(2, 6)
arr.reverse()
print(arr)
“`

### 8. Add, transpose, and multiply two matrices:
“`python
import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

# Add
print(np.add(A, B))

# Transpose
print(A.T)

# Multiply
print(np.dot(A, B))
“`

### 9. Min, max, sum, and cumulative sum of an array:
“`python
arr = [1, 2, 3, 4, 5]
print(min(arr), max(arr), sum(arr))
print(np.cumsum(arr))
“`

### 10. Dictionary with lists converted to a pandas DataFrame:
“`python
import pandas as pd
data = {
‘A’: [1,2,3,4,5,6,7,8,9,10],
‘B’: [11,12,13,14,15,16,17,18,19,20],
‘C’: [21,22,23,24,25,26,27,28,29,30],
‘D’: [31,32,33,34,35,36,37,38,39,40],
‘E’: [41,42,43,44,45,46,47,48,49,50]
}
df = pd.DataFrame(data)

# a) head() function
print(df.head())

# b) Data selection
print(df[‘A’])
print(df.iloc[1:4, 2:4])
“`

This program covers all tasks in a compact form.