Complex Numbers Yr 2 Flashcards
1
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What is De Moivre’s Theorem?
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2
Q
Prove De Moivre’s Theorem by induction
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7
Q
What is the equation to the roots of z^n =1
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8
Q
How are the nth roots of unity shown on a complex number diagram?
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9
Q
What is the sum of the roots of unity?
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Always = 0
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12
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What is the equation of roots of any complex number?
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14
Q
Derive the equation for the nth roots of unity
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15
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Derive the formula of equation for complex roots of any complex number
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21
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What is the form of e^i°?
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23
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What is Euler’s identity?
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24
Q
What are the two important identities for sin and cos in terms of e^° and i ?
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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
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Derive the nth roots of unity formula
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General nth roots of unity formula
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.
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Derive the nth roots for any complex number formula
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What is the general formula for the nth roots of any complex number ?
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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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Complete the identities
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Don’t forget the pi and the i !
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Part a
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Part b
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Exam practice
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Part a
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Part A
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