# Quiz 1 (Complex Numbers)

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Quizzes Created: 3 | Total Attempts: 9,747
Questions: 12 | Attempts: 805

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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)

• 1.

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

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.
B. 2cos
Explanation
Hence,    (shown)

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• 4.
• A.

True

• B.

False

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

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

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.

5
• 8.

### If   what is the value of

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?

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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• 10.

### The equation must have 3 pairs of complex conjugate roots.

• A.

True

• B.

False

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.
0
Explanation
Recognise that , therefore   (shown)

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• 12.

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

1
Explanation
Hence, we have a=1 (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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