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Table of contents

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0. Review of College Algebra4h 31m
1. Measuring Angles39m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Laws of Sines, Cosines and VectorsComing soon
8. Complex Numbers, Polar Coordinates and Parametric EquationsComing soon

0. Review of College Algebra

Complex Numbers

0. Review of College Algebra

Complex Numbers - Video Tutorials & Practice Problems

Previous Topic: Solving Quadratic Equations

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1

concept

Introduction to Complex Numbers

Video duration:

3m

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2

Problem

Problem

Identify the real and imaginary parts of each complex number.
$-4-9i$

A

$a = -9, b = -4$

B

$a = -4, b = -9$

C

$a = 4, b = 9$

D

$a = -4, b = 9$

3

Problem

Problem

Identify the real and imaginary parts of each complex number.
$3+2i\sqrt3$

A

$a=3,b=2\sqrt3$

B

$a = 3, b = 2$

C

$a=2\sqrt3,b=3$

D

$a=3,b=\sqrt3$

4

Problem

Problem

Write the complex number in standard form.
$\frac{9+\sqrt{-16}}{3}$

A

$3+4i$

B

$9+16i$

C

$3+\frac43i$

D

$\frac{13i}{3}$

5

concept

Adding and Subtracting Complex Numbers

Video duration:

3m

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6

Problem

Problem

Find the difference. Express your answer in standard form.
$\left(2+8i\right)-\left(4-i\right)$

A

$-2+9i$

B

$6+7i$

C

$2+7i$

D

$2-9i$

7

Problem

Problem

Find the sum. Express your answer in standard form.
$5\left(4+7i\right)+6\left(3-2i\right)$

A

$7+5i$

B

$38+23i$

C

$2+47i$

D

$7+9i$

8

concept

Multiplying Complex Numbers

Video duration:

5m

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9

Problem

Problem

Perform the indicated operation. Express your answer in standard form.
$\left(3+8i\right)^2$

A

$-55+48i$

B

$9+64i$

C

$24i$

D

$9+24i$

10

Problem

Problem

Find the product. Express your answer in standard form.
$2i\left(9-4i\right)\left(6+5i\right)$

A

$8+18i$

B

$54-20i$

C

$54-40i$

D

$-42+148i$

11

concept

Complex Conjugates

Video duration:

5m

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12

Problem

Problem

Find the product of the given complex number and its conjugate.
$4-5i$

A

16

B

41

C

25

D

20

13

Problem

Problem

Find the product of the given complex number and its conjugate.
$-7-i$

A

$50$

B

$14$

C

$49$

D

$1$

14

concept

Dividing Complex Numbers

Video duration:

4m

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15

Problem

Problem

Find the quotient. Express your answer in standard form.
$\frac{6+i}{4-2i}$

A

$\frac{11}{10}+\frac45i$

B

$\frac65+\frac45i$

C

$\frac{11}{10}-\frac45i$

D

$22+16i$

16

Problem

Problem

Find the quotient. Express your answer in standard form.
$\frac{-5+3i}{-7-4i}$

A

$\frac35+\frac45i$

B

$18i$

C

$23-41i$

D

$\frac{23}{65}-\frac{41}{65}i$

Do you want more practice?

We have more practice problems on Complex Numbers

Previous Topic: Solving Quadratic Equations

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