1
Q
What is De Moivre’s Theorem?
A
2
Q
Prove De Moivre’s Theorem by induction
A
3
Q
A
4
Q
A
5
Q
A
6
Q
A
7
Q
What is the equation to the roots of z^n =1
A
8
Q
How are the nth roots of unity shown on a complex number diagram?
A
9
Q
What is the sum of the roots of unity?
A
Always = 0
10
Q
A
11
Q
A
12
Q
What is the equation of roots of any complex number?
A
13
Q
A
14
Q
Derive the equation for the nth roots of unity
A
15
Q
Derive the formula of equation for complex roots of any complex number
A
16
Q
A
17
Q
A
18
Q
A
19
Q
A
20
Q
A
21
Q
What is the form of e^i°?
A
22
Q
A
23
Q
What is Euler’s identity?
A
24
Q
What are the two important identities for sin and cos in terms of e^° and i ?
A
25
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32
What are the nth roots of unity?
Complex numbers that when raised to the nth power, equal 1. Each root represents a point on the complex plane on the unit circle, creating a regular polygon with n vertices
33
Derive the nth roots of unity formula
34
General nth roots of unity formula
35
.
36
Derive the nth roots for any complex number formula
37
What is the general formula for the nth roots of any complex number ?
38
What is the nth roots for any complex number?
Similar to the nth roots of unity but instead of lying on a unit circle, they lie on a circle at with radius r^1/n and starting at angle theta/n, rather than at 1,0
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49
Complete the identities
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59
Don’t forget the pi and the i !
60
61
Part a
62
Part b
63
Exam practice
64
Part a
65
66
Part A
67
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70
A Level Further Maths Pure
flashcards
Decks in class (18)
# Cards
-
Series And Sequences40
-
Matrices (pt2)63
-
Complex numbers23
-
Roots of Polynomials24
-
The argand Diagram47
-
Vectors33
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Vectors Year 216
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Matricies Yr217
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Complex Numbers Yr 270
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Polar Co-ordinates Yr234
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Further Calculus Yr246
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Maclaurin Series30
-
Hyperbolic Functions48
-
Complex Numbers45
-
Differential Equations (1st Order)36
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Further Calculus19
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Differential Equations (2nd Order)19
-
Volumes Of Revolution10
