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Number systems

Written by Hassan Raza (Mathematics)

Class 11 · Mathematics · 8 questions

Name: ____________________   Date: ____________

  1. Which of these is a rational number?

    • A pi
    • B The square root of 5
    • C 0.75
    • D The square root of 3

  2. i to the power 4 equals:

    • A i
    • B -1
    • C 1
    • D -i

  3. (1 + i)(1 - i) equals:

    • A -2
    • B 0
    • C 2
    • D 1 - i²

  4. The modulus of 3 + 4i is:

    • A 5
    • B 1
    • C 25
    • D 7

  5. The multiplicative inverse of 2 + i is:

    • A 1 / 2
    • B (2 + i) / 5
    • C (2 - i) / 5
    • D 2 - i

  6. The conjugate of 5 - 2i is:

    • A -5 + 2i
    • B -5 - 2i
    • C 2 - 5i
    • D 5 + 2i

  7. The value of i³ is:

    • A 1
    • B -i
    • C -1
    • D i

  8. The modulus of -3 + 4i is:

    • A 7
    • B 25
    • C 1
    • D 5

Answer key

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

  1. 0.75 = 3/4.

  2. i² = -1, so i⁴ = 1.

  3. 1 - i² = 1 + 1 = 2.

  4. Square root of (9 + 16) = 5.

  5. 1 / (2 + i) = (2 - i) / (4 + 1) = (2 - i) / 5.

  6. Change the sign of the imaginary part.

  7. i³ = i² x i = -i.

  8. Square root of (9 + 16) = 5.