حقیقی اور مخلوط اعداد

Written by Hassan Raza (Mathematics)

نویں جماعت · ریاضی · 10 سوالات

نام: ____________________ تاریخ: ____________

Which of these is an irrational number?
- A The square root of 2
- B 4
- C 3/4
- D 0.5
What is i squared, where i is the imaginary unit?
- A 0
- B -1
- C i
- D 1
What is (2 + 3i) + (4 - i)?
- A 2 + 2i
- B 8 + 3i
- C 6 + 4i
- D 6 + 2i
What is the conjugate of 3 + 4i?
- A -3 + 4i
- B 3 - 4i
- C -3 - 4i
- D 4 + 3i
Which property is shown by a + b = b + a?
- A Commutative
- B Associative
- C Identity
- D Distributive
What is the additive identity of real numbers?
- A 0
- B Infinity
- C -1
- D 1
Which of these is a natural number?
- A 0.7
- B 7
- C 7/3
- D -7
The product of a rational and an irrational number (non zero rational) is:
- A Rational
- B Irrational
- C Integer
- D Zero
What is (3 + 2i) - (1 + 5i)?
- A 4 - 3i
- B 2 - 3i
- C 2 + 3i
- D 4 + 7i
Which number is both rational and an integer?
- A 1/2
- B 5
- C Square root of 2
- D pi

جوابی کلید

1. A, 2. B, 3. D, 4. B, 5. A, 6. A, 7. B, 8. B, 9. B, 10. B

The square root of 2 cannot be written as a ratio of two integers.
By definition i² = -1.
Add real parts: 2 + 4 = 6. Add imaginary parts: 3 - 1 = 2.
The conjugate changes the sign of the imaginary part.
Changing the order of addition does not change the result: the commutative property.
Adding 0 to any number leaves it unchanged.
Natural numbers are 1, 2, 3, ...
For example 2 times the square root of 2 is irrational.
Subtract the real and imaginary parts.
5 is an integer.