Chapter 16 - Complex Numbers 2

Question 1

State Euler’s Formula.

Answer 1

Question 2

Define cosθ and sinθ as exponentials.

Answer 2

Only works for radians.

Question 3

State the equation for finding the roots of unity.

Answer 3

For complex numbers with two parts, replace 2kπ with 2kπ + (arg) and insert coefficient behind e (the modulus)

Question 4

Using ω, explain the sum of the roots of unity.

Answer 4

This is a geometric sequence.

Question 5

Using Euler’s Formula, what is the equivalent of this?

Answer 5

Question 6

Using Euler’s Formula, what is the equivalent of this?

Answer 6

Question 7

Using Euler’s Formula, what is the equivalent of this?

Answer 7

Question 8

Using Euler’s Formula, what is the equivalent of this?

Answer 8

Question 9

Express a complex number, zⁿ, in exponential form.

Answer 9

Question 10

State de Moivre’s theorem.

Answer 10