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Complex Numbers and Their Properties

Complex Numbers and Their Properties

Assessment

Interactive Video

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to solve the equation Z to the power of 8 minus 1 equals zero using complex numbers. It covers the modulus and polar form of complex numbers, and demonstrates how to find the eight roots of the equation. The tutorial concludes with a visualization of these roots on the unit circle, showing their positions at equal intervals.

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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation we are trying to solve using complex numbers?

Z^8 = 0

Z^8 = 1

Z^8 - 1 = 0

Z^8 + 1 = 0

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the modulus of W when W = Z^8 = 1?

0

1

2

Infinity

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can W be expressed in polar form?

W = tan(0) + i cot(0)

W = cos(0) + i sin(0)

W = sec(0) + i csc(0)

W = sin(0) + i cos(0)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many possible values of Z are there when solving Z^8 = 1?

10

8

6

4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of Z when K=0?

i

1

-1

0

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of Z when K=1?

1/sqrt(2) + i/sqrt(2)

-1/sqrt(2) - i/sqrt(2)

-1/sqrt(2) + i/sqrt(2)

1/sqrt(2) - i/sqrt(2)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of Z when K=2?

-1

i

-i

1

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