Complex Number Roots and Properties

The video tutorial explains the concept of finding the Nth roots of complex numbers, using De Moivre's Theorem. It begins with an introduction to complex roots and demonstrates finding the cubed roots of 8, showing their even distribution on the complex plane. The Nth Root Theorem is introduced, followed by a detailed example of finding the 4th roots of a complex number. The process involves converting the number to trigonometric form, calculating angles, and evaluating the roots. The tutorial concludes with verifying the results, emphasizing the even distribution of roots.

What is the main goal of the video presentation?

• To determine the Nth roots of a complex number

• To discuss real numbers

• To solve linear equations

• To explain the history of complex numbers

Tags

CCSS.HSN.CN.A.1

How many distinct complex roots does a non-zero complex number have for a given positive integer N?

• N+1 distinct roots

• N distinct roots

• N-1 distinct roots

• 2N distinct roots

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CCSS.8.EE.A.2

What is one of the cube roots of 8?

• X = 4

• X = 2

• X = 3

• X = 1

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CCSS.HSN.CN.A.3

Which formula is used to find the roots of a complex number when it is not factorable?

• Linear formula

• Quadratic formula

• Cubic formula

• Exponential formula

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CCSS.HSN.CN.A.3

How are the roots of a complex number distributed on the complex plane?

• In a circle

• Evenly

• In a straight line

• Randomly

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CCSS.HSN.CN.A.3

What is the value of K when finding the 4th roots of a complex number?

• 0, 1, 2, 4

• 1, 2, 3, 5

• 1, 2, 3, 4

• 0, 1, 2, 3

Tags

CCSS.HSN.CN.A.3

What is the first step in finding the 4th roots of a complex number?

• Solving a linear equation

• Calculating the square root

• Writing the complex number in trigonometric form

• Finding the value of K

What is the value of R for the complex number -8 + 8i√3?

• 16

• 8

• 32

• 4

What is the angle θ for the complex number -8 + 8i√3?

• 60 degrees

• 180 degrees

• 90 degrees

• 120 degrees

What is the 4th root of 16?

• 1

• 8

• 2

• 4