Chapter 16 - Complex Numbers 2 Flashcards
Exponential Form, De Moivre's Theorem, Roots of Unity. This A-Level Topic is far from e-z*. So keep up!
1
Q
State Euler’s Formula.
A
2
Q
Define cosθ and sinθ as exponentials.
A
Only works for radians.
3
Q
State the equation for finding the roots of unity.
A
For complex numbers with two parts, replace 2kπ with 2kπ + (arg) and insert coefficient behind e (the modulus)
4
Q
Using ω, explain the sum of the roots of unity.
A
This is a geometric sequence.
5
Q
Using Euler’s Formula, what is the equivalent of this?
A
6
Q
Using Euler’s Formula, what is the equivalent of this?
A
7
Q
Using Euler’s Formula, what is the equivalent of this?
A
8
Q
Using Euler’s Formula, what is the equivalent of this?
A
9
Q
Express a complex number, zⁿ, in exponential form.
A
10
Q
State de Moivre’s theorem.
A
