Quiz 1 (Complex Numbers)

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| By Whitecorp

Whitecorp

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Quizzes Created: 3 | Total Attempts: 9,061

Questions: 12 | Attempts: 798 | Updated: Mar 21, 2023

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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 .
- A.
- B.
- C.
- D.
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."

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3.

If what is
- A.
  
  Not possible to tell
- B.
  
  2cos
- C.
- D.
Correct Answer
B. 2cos

Explanation
Hence, (shown)

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4.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
(shown)

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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)

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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)

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7.

What is the value of

Correct Answer
5
8.

If what is the value of
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
(shown)

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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.

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0
4 1
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.

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11.

Correct Answer
0

Explanation
Recognise that , therefore (shown)

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4
12.

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

Correct Answer
1

Explanation
Hence, we have a=1 (shown)

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4