Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem

Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem

Assessment

Interactive Video

Mathematics, Engineering, Science

11th Grade - University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial introduces complex numbers, explaining their components: real and imaginary parts. It covers the imaginary unit 'i', its powers, and how complex numbers are expressed in standard form. The tutorial demonstrates operations with complex numbers, including addition, subtraction, multiplication, and division, emphasizing the use of complex conjugates. It also discusses the application of complex numbers in solving polynomials, highlighting the linear factorization theorem.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the imaginary unit 'i' defined as?

The square root of 1

The square root of -1

The square root of 0

The square root of 2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is a complex number generally expressed?

a * bi

a / bi

a - bi

a + bi

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens when you add 2 + i and 3 - i?

1 + 2i

1 + 0i

5 + 2i

5 + 0i

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of multiplying a complex number by its conjugate?

Zero

A real number

An imaginary number

A complex number

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the complex conjugate of 4 + 3i?

-4 - 3i

4 - 3i

4 + 3i

-4 + 3i

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of polynomials, what does the linear factorization theorem state?

A polynomial of degree n has n imaginary factors

A polynomial of degree n has n real factors

A polynomial of degree n has n linear factors

A polynomial of degree n has n unique factors

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of solutions do quadratics with no real solutions have?

Imaginary solutions

Complex conjugate solutions

No solutions

Real solutions

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