Complex Cube Roots of Unity and Probability

The video tutorial explores the concept of complex cube roots of unity, focusing on the properties and powers of omega, a complex cube root. It sets up a probability problem involving rolling a die and calculating the probability that the sum of certain powers of omega equals zero. The tutorial walks through the steps of determining the possible outcomes and their probabilities, ultimately finding the probability to be 2/9.

What is a complex cube root of unity that is not equal to 1?

• 2

• i

• 1

• omega

What is the value of omega cubed?

• omega

• 0

• omega squared

• 1

What is omega to the fourth power equivalent to?

• omega

• 1

• omega cubed

• omega squared

Which power of omega is equivalent to omega squared?

• omega to the fifth

• omega to the fourth

• omega cubed

• omega to the sixth

In the probability problem, what is the sum of powers of omega expected to equal?

• 1

• 0

• omega

• omega squared

How many different ways can the die rolls be arranged to achieve the desired sum?

• 9

• 6

• 12

• 3

What is the probability that the sum of the powers of omega equals zero?

• 1/3

• 1/6

• 2/9

• 1/9

What is the probability that r1 is either 1 or 4?

• 1/6

• 1/4

• 1/3

• 1/2

What is the probability that r2 is either 5 or 2?

• 1/6

• 1/4

• 1/5

• 1/3

What is the probability that r3 is either 3 or 6?

• 1/3

• 1/5

• 1/2

• 1/4