In the given expressions; √(-5)², -12, 2, -7i² are pure real numbers, while ( -i² + i³), (7 - 5i), (√-6), (0 + 9i) are non-real complex numbers.
Analysing each expression to determine if it represents a purely real number or a non-real complex number:
1. -i² + i³:
-i² + i³ = -(-1) + i(-1)
= 1 - i
This expression represents a non-real complex number.
2. 7 - 5i: This expression has both a real part (7) and an imaginary part (-5i).
This expression a non-real complex number.
3. √(-6): The square root of a negative number is not a real number.
This expression represents a non-real complex number.
4. 0 + 9i: This expression has only an imaginary part (9i).
This expression represents a non-real complex number.
5. √(-5)²:
(√-5)² = √25
= 5
This expression represents a purely real number.
6. -12: This is a real number.
This expression represents a purely real number.
7. 2: This is a real number.
This expression represents a purely real number.
8. -7i²:
-7i² = -7(-1)
= 7
This expression represents a purely real number.
Therefore:
- Purely Real Numbers: √(-5)², -12, 2, -7i² are pure real numbers.
- Non-Real Complex Numbers: ( -i² + i³), (7 - 5i), (√-6), (0 + 9i) are non-real complex numbers.