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Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2

purely real number


non-real complex number

Determine which expressions represent purely real numbers and which expressions represent-example-1
User Sohil Pandya
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1 Answer

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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.

User Gat
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