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Quiz

Lesson 1: Complex Numbers in Trigonometric and Exponential Form and De Moivres Theorem — Picture questions (exam style)

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  • Questions count: 46
  • Passing grade: 60%
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1.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 4, |z4| = 1
least n making zn real = 8, |z4| = 2
least n making zn real = 3, |z4| = 4
least n making zn real = 8, |z4| = 1
2.
If ω is a non-real cube root of unity, what is (1 + ω)39?
If ω is a non-real cube root of unity, what is (1 + ω)^39?
−ω
−1
−ω2
ω
3.
What is the real part of z2?
What is the real part of z^2?
12
-6
10.39
6
4.
What is the sum of the roots shown?
What is the sum of the roots shown?
12
1
0
64
5.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 10, |z5| = 11.31
least n making zn real = 10, |z5| = 8
least n making zn real = 4, |z5| = 5.657
least n making zn real = 5, |z5| = 5.657
6.
What is the principal argument of z4 (degrees)?
What is the principal argument of z^4 (degrees)?
-120 °
-116 °
-480 °
60 °
7.
What is the angle between consecutive 5th roots shown?
What is the angle between consecutive 5th roots shown?
36 °
72 °
18 °
90 °
8.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 5, |z6| = 6
least n making zn real = 5, |z6| = 1
least n making zn real = 6, |z6| = 2
least n making zn real = 6, |z6| = 1
9.
By de Moivre’s theorem, what is |z3|?
By de Moivre’s theorem, what is |z^3|?
124.7
10.39
41.57
12
10.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 9, |z6| = 64
least n making zn real = 12, |z6| = 128
least n making zn real = 6, |z6| = 64
least n making zn real = 5, |z6| = 128
11.
What is the principal argument of z6 (degrees)?
What is the principal argument of z^6 (degrees)?
180 °
-114 °
-720 °
0 °
12.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 24, |z12| = 90.51
least n making zn real = 11, |z12| = 16.97
least n making zn real = 12, |z12| = 90.51
least n making zn real = 12, |z12| = 64
13.
What is the principal argument of z (degrees)?
What is the principal argument of z (degrees)?
150 °
-30 °
30 °
120 °
14.
What is the sum of the roots shown?
What is the sum of the roots shown?
9
27
1
0
15.
By de Moivre’s theorem, what is |z2|?
By de Moivre’s theorem, what is |z^2|?
3.464
6
3
1.732
16.
What is the angle between consecutive 5th roots shown?
What is the angle between consecutive 5th roots shown?
36 °
72 °
54 °
126 °
17.
What is the principal argument of z5 (degrees)?
What is the principal argument of z^5 (degrees)?
240 °
150 °
60 °
125 °
18.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 1, |z2| = 2
least n making zn real = 2, |z2| = 1
least n making zn real = 2, |z2| = 2
least n making zn real = 4, |z2| = 1
19.
By de Moivre’s theorem, what is |z2|?
By de Moivre’s theorem, what is |z^2|?
18
3
9
6
20.
What is the angle between consecutive 6th roots shown?
What is the angle between consecutive 6th roots shown?
30 °
120 °
60 °
0 °
21.
By de Moivre’s theorem, what is |z3|?
By de Moivre’s theorem, what is |z^3|?
1
1.74
3
2.11
22.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 4, |z4| = 2
least n making zn real = 8, |z4| = 4
least n making zn real = 4, |z4| = 1
least n making zn real = 8, |z4| = 1
23.
What is the sum of the roots shown?
What is the sum of the roots shown?
16
0
8.706
1
24.
The 5th roots of the number shown are plotted. What is the modulus of each root?
The 5th roots of the number shown are plotted. What is the modulus of each root?
7.579
1.516
1.6
8
25.
The 6th roots of the number shown are plotted. What is the modulus of each root?
The 6th roots of the number shown are plotted. What is the modulus of each root?
10.39
27
1.732
4.5
26.
What is the principal argument of z4 (degrees)?
What is the principal argument of z^4 (degrees)?
-146 °
-60 °
120 °
-600 °
27.
What is the principal argument of z (degrees)?
What is the principal argument of z (degrees)?
135 °
45 °
78.3 °
-45 °
28.
What is the real part of z6?
What is the real part of z^6?
27
1
0
0.5
29.
What is the principal argument of z2 (degrees)?
What is the principal argument of z^2 (degrees)?
-300 °
60 °
-120 °
-148 °
30.
What is the sum of the roots shown?
What is the sum of the roots shown?
1
27
0
10.39
31.
What is the modulus of the complex number z shown on the Argand diagram?
What is the modulus of the complex number z shown on the Argand diagram?
4.243
9
1.5
3
32.
The 4th roots of the number shown are plotted. What is the modulus of each root?
The 4th roots of the number shown are plotted. What is the modulus of each root?
2
1.682
6.727
8
33.
What is the principal argument of z (degrees)?
What is the principal argument of z (degrees)?
45 °
135 °
-78.3 °
-45 °
34.
By de Moivre’s theorem, what is |z3|?
By de Moivre’s theorem, what is |z^3|?
5.196
15.59
9.041
3
35.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 12, |z6| = 11.31
least n making zn real = 6, |z6| = 8
least n making zn real = 9, |z6| = 8
least n making zn real = 6, |z6| = 8.485
36.
What is the principal argument of z (degrees)?
What is the principal argument of z (degrees)?
-45 °
234.9 °
135 °
-135 °
37.
z is shown on the Argand diagram. Which option is correct?
z is shown on the Argand diagram. Which option is correct?
least n making zn real = 4, |z4| = 16
least n making zn real = 7, |z4| = 32
least n making zn real = 3, |z4| = 16
least n making zn real = 8, |z4| = 32
38.
What is the sum of the roots shown?
What is the sum of the roots shown?
27
1
0
9.666
39.
By de Moivre’s theorem, what is |z4|?
By de Moivre’s theorem, what is |z^4|?
9
5.196
36
6.928
40.
What is the principal argument of z3 (degrees)?
What is the principal argument of z^3 (degrees)?
135 °
-45 °
48 °
-135 °
41.
The 6th roots of the number shown are plotted. What is the modulus of each root?
The 6th roots of the number shown are plotted. What is the modulus of each root?
1.414
1.333
8.485
8
42.
What is the principal argument of z3 (degrees)?
What is the principal argument of z^3 (degrees)?
90 °
-90 °
-180 °
33 °
43.
What is the modulus of the complex number z shown on the Argand diagram?
What is the modulus of the complex number z shown on the Argand diagram?
2.828
8
1.414
4.921
44.
What is the principal argument of z5 (degrees)?
What is the principal argument of z^5 (degrees)?
-60 °
120 °
-150 °
65 °
45.
What is the real part of z2?
What is the real part of z^2?
0
8
-8
1
46.
What is the real part of z3?
What is the real part of z^3?
22.63
-22.63
0
39.37
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