Quiz 1 (Complex Numbers)

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
Learn about Our Editorial Process
| By Whitecorp
W
Whitecorp
Community Contributor
Quizzes Created: 3 | Total Attempts: 9,747
Questions: 12 | Attempts: 805

SettingsSettingsSettings
Quiz 1 (Complex Numbers) - 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)


Questions and Answers
  • 1. 

    Express in the form .

    Correct Answer
    A.
  • 2. 

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

    • A.

      It is not a circle but a perpendicular bisector

    • B.

      2 units

    • C.

      units

    • D.

      1 unit

    Correct Answer
    B. 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."

    Rate this question:

  • 3. 

    If what is

    • A.

      Not possible to tell

    • B.

      2cos

    • C.
    • D.
    Correct Answer
    B. 2cos
    Explanation
    Hence,    (shown)

    Rate this question:

  • 4. 

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
      (shown)

    Rate this question:

  • 5. 

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

    • A.

      30

    • B.

      40

    • C.
    • D.

      50

    Correct Answer
    D. 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)

    Rate this question:

  • 6. 

    If     ,  what is the value of 

    • A.

      0

    • B.

      1

    • C.

      2

    • D.

      6

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

    Rate this question:

  • 7. 

    What is the value of

    Correct Answer
    5
  • 8. 

    If   what is the value of

    Correct Answer
    B.
    Explanation
      (shown)

    Rate this question:

  • 9. 

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

    Correct Answer
    71
    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.

    Rate this question:

  • 10. 

    The equation must have 3 pairs of complex conjugate roots.

    • A.

      True

    • B.

      False

    Correct Answer
    B. 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.

    Rate this question:

  • 11. 

    Correct Answer
    0
    Explanation
    Recognise that , therefore   (shown)

    Rate this question:

  • 12. 

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

    Correct Answer
    1
    Explanation
    Hence, we have a=1 (shown)

    Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

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

Related Topics

Back to Top Back to top
Advertisement