Booleans in Python

bool(1j)

“Is the complex number 1j considered True or False?”

- 1j is a complex number with real part 0 and imaginary part 1.

- In Python, any nonzero number (whether int, float, or complex) evaluates to True when converted to bool.

- Only 0, 0.0, or 0j (complex zero) evaluate to False.

A complex number is a number that has two parts:

z=a+bj

• a → the real part (ordinary number line)
• b → the imaginary part (multiplied by j in Python, or i in mathematics)

Key ideas

• The imaginary unit j (or i in math) is defined as \sqrt{-1}.
• Complex numbers extend the real numbers so we can solve equations like x^2+1=0, which has no real solution but has complex solutions x=\pm i.

Visual intuition

You can think of complex numbers as points on a 2D plane:

• The horizontal axis = real part
• The vertical axis = imaginary part
  So 3+4j is the point (3, 4).

bool('')

you’re converting an empty string ('') into a boolean value.

Rule

• Empty sequences/collections (like '', [], {}, ()) evaluate to False.
• Non-empty sequences/collections (like 'hello', [1], (0,)) evaluate to True.

[] → List

• A list is an ordered, mutable sequence of elements.
• You can store mixed types (numbers, strings, other lists).
• Lists allow indexing, slicing, and modification

my_list = [1, 2, 3, "hello"]

my_list.append(4)       # add element

print(my_list[0])       # access first element → 1




"hello" is indeed the fourth element (index 3, since Python starts counting at 0). 




{} → Dictionary (or empty set, depending on usage)

• By default, {} creates an empty dictionary.
• A dictionary stores key-value pairs.
• Keys must be unique and immutable (like strings, numbers, tuples).

my_dict = {"name": "Alice", "age": 25}

print(my_dict["name"])   # → Alice




() → Tuple

• A tuple is an ordered, immutable sequence.
• Similar to a list, but you cannot change its contents after creation.
• Often used for fixed collections of items.

my_tuple = (10, 20, 30) print(my_tuple[1]) # → 20

Data structures include list, tuple, dictionary and set.

explicit: clear and easy to understand, so that you have no doubt what is meant

a = 5

b = 5

if a - b:

    print('a and b are not equal!')

No output will be printed.

weatherIsNice = True

haveUmbrella = False

if not (haveUmbrella or weatherIsNice):

    print('Stay inside')

else:

    print('Go for a walk')

1. weatherIsNice = True

2. haveUmbrella = False

3. Inside the if condition:

-(haveUmbrella or weatherIsNice) → evaluates to (False or True) → True.

-not (True) → False.

4. Since the condition is False, the else block runs.

Logic explained

• The condition says: “If you do not have an umbrella and the weather is not nice, then stay inside.”
• In this case, the weather is nice, so you can go for a walk even without an umbrella.

weatherIsNice = True

haveUmbrella = False

if (not haveUmbrella) and (not weatherIsNice):

    print('Stay inside')

else:

    print('Go for a walk')

Logic

This condition means:

• “Stay inside only if you don’t have an umbrella and the weather is not nice.”
• In this case, the weather is nice, so you go for a walk.

weatherIsNice = True

haveUmbrella = False

if haveUmbrella or weatherIsNice:

    print('Go for a walk')

else:

    print('Stay inside')

Logic

This condition means:

• “If you either have an umbrella or the weather is nice, then go for a walk.”
• Only if both are false (no umbrella and bad weather) will it print “Stay inside.”

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