Quiz 1 (Complex Numbers)

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Quiz 1 (Complex Numbers) - Quiz
About This Quiz

This is a complex numbers quiz. There are altogether 12 questions; maximum recommended time limit for completion is 4 minutes (or 20 seconds per question). NO CALCULATORS SHALL BE USED. Peace.
A WHITE GROUP MATHEMATICS CREATION (www. Whitegroupmaths. Com)

Quiz Preview

  • 2. 
      , where a is an integer. What is the value of a? - ProProfs

      , where a is an integer. What is the value of a?

    Explanation
    Hence, we have a=1 (shown)

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  • 3. 
    The roots of this quadratic equation   are where k is a positive integer. What is the value of k? - ProProfs

    The roots of this quadratic equation   are where k is a positive integer. What is the value of k?

    Explanation
    The value of k is 71 because the question states that the roots of the quadratic equation are where k is a positive integer. Therefore, since k is a positive integer and the only option given is 71, the value of k must be 71.

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  • 4. 
    What is the value of - ProProfs

    What is the value of

  • 5. 
    - ProProfs

    • True

    • False

    Correct Answer
    A. False
    Explanation
      (shown)

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  • 6. 
    Express in the form . - ProProfs

    Express in the form .

    Correct Answer
    A.
  • 7. 

    What is (2+i)(2-i)(3+i)(3-i) ?

    • 30

    • 40

    • Quiz 1 (Complex Numbers) - Quiz

    • 50

    Correct Answer
    A. 50
    Explanation
    Note that the property is used here:
    (2+i)(2-i)(3+i)(3-i) = [(2+i)(2-i)] [(3+i)(3-i)] = (5)(10)=50 (shown)

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  • 8. 
    If what is - ProProfs

    If what is

    • Not possible to tell

    • 2cos

      Quiz 1 (Complex Numbers) - Quiz

    • Quiz 1 (Complex Numbers) - Quiz

    • Quiz 1 (Complex Numbers) - Quiz
    Correct Answer
    A. 2cos
    Explanation
    Hence,    (shown)

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  • 9. 
    If     ,  what is the value of  - ProProfs

    If     ,  what is the value of 

    • 0

    • 1

    • 2

    • 6

    Correct Answer
    A. 0
    Explanation
        since     (shown)
    (Note the above series is a GP with common ratio z and first term 1)

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  • 10. 
    The equation must have 3 pairs of complex conjugate roots. - ProProfs

    The equation must have 3 pairs of complex conjugate roots.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    The statement is false because a quadratic equation can have either two distinct real roots or two complex conjugate roots. It cannot have three pairs of complex conjugate roots as that would imply a total of six roots, which is not possible for a quadratic equation.

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  • 11. 
    For the equation where z denotes a variable complex number in Argand space, what is the radius of the circle represented by this loci? - ProProfs

    For the equation where z denotes a variable complex number in Argand space, what is the radius of the circle represented by this loci?

    • It is not a circle but a perpendicular bisector

    • 2 units

    • units

      Quiz 1 (Complex Numbers) - Quiz

    • 1 unit

    Correct Answer
    A. 2 units
    Explanation
    The given equation represents the perpendicular bisector of a line segment in the Argand space. The perpendicular bisector is a line that intersects the line segment at a right angle and divides it into two equal parts. Since the equation does not represent a circle, the concept of radius does not apply. Therefore, the correct answer is "It is not a circle but a perpendicular bisector."

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  • 12. 
    If   what is the value of - ProProfs

    If   what is the value of

    Correct Answer
    A.
    Explanation
      (shown)

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 09, 2012
    Quiz Created by
    Whitecorp
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