An Introduction to Complex Numbers

سرفصل های دوره

Explains why we need it and how to work with it.

1. Introduction

1. Who are you

2. What are you going to teach me

3. How do I get the best out of this course

4. Why should I learn about complex numbers

5. How do I know when to use complex numbers

6. How do I find the square root of a number less than zero

7. What is a complex number

8. What is a complex conjugate

9. What did I learn from this section

10.1 introduction-exercise.pdf

10.2 introduction-solution.pdf

10. Introductory Exercise

2. Cartesian form

1. What is the Cartesian form of a complex number

2. How do I calculate powers of i

3. How do I work with complex numbers in Cartesian form

4. How do I add complex numbers in Cartesian form

5. How do I subtract complex numbers in Cartesian form

6. How do I multiply complex numbers in Cartesian form

7. How do I determine the power of a complex number in Cartesian form

8. How do I divide by a complex number in Cartesian form

9. How do I solve for unknown variables with complex numbers

10. How do I calculate the square root of a complex number in Cartesian form

11. How do I solve quadratic equations with complex coefficients

12. How do I verify that the complex roots from my quadratic equations are correct

13. What did I learn from this section

14.1 cartesian-form-exercise.pdf

14.2 cartesian-form-solution.pdf

14. Cartesian Form Exercise

3. Argand Diagrams

1. What is an Argand diagram

2. How do I add complex numbers with an Argand diagram

3. How do I subtract complex numbers with an Argand diagram

4. How do I multiply complex numbers with an Argand diagram

5. How to divide complex numbers represented on an argand diagram

6. What did I learn from this section

7.1 argand-diagram-exercise.pdf

7.2 argand-diagram-solutions.pdf

7. Argand Diagram Exercise

4. Polar form

1. What is the polar form of a complex number

2. How do I calculate the modulus of a complex number

3. How do I calculate the argument of a complex number

4. How do I convert the Cartesian form of a complex number to Polar form

5. How do I express the conjugate of the polar form

6. How do I add complex numbers in polar form

7. How do I subtract complex numbers in polar form

8. How do I multiply complex numbers in polar form

9. What is De Moivres theorem

10. How do I use De Moivres theorem

11. How do I use De Moivres theorem to express trigonometric ratios in other forms

12. How do I divide complex numbers in polar form

13. What did I learn in this section

14.1 polar-form-exercise.pdf

14.2 polar-form-solutions.pdf

14. Polar form exercise

5. Locus of a variable complex point

1. What is the locus of a variable complex point

2. How do I find out if the locus is a circle

3. How do I find out if the locus is a straight line

4. How do I find out if the locus is a half-line ray

5. How do I find out if the locus is a semi-circle

6. How do I find out if the locus is a minor arc

7. How do I find out if the locus is a major arc

8. How do I find the intersection point of two loci

9. How do I find the region of interest with complex number inequalities

10. What did I learn from this section

11.1 locus-of-a-variable-complex-point-exercise.pdf

11.2 locus-of-a-variable-complex-point-solution.pdf

11. Variable Complex Point Exercise.html

6. Exponential form

1. What is Eulers formula

2. How do I use Eulers formula

3. How do I add complex numbers in exponential form

4. How do I subtract complex numbers in exponential form

5. How do I multiply complex number in exponential form

6. How do I calculate powers of a complex number in exponential form

7. How do I divide complex numbers in exponential form

8. What did I learn from this section

9.1 locus-of-a-variable-complex-point-exercise.pdf

9.2 locus-of-a-variable-complex-point-solution.pdf

9. Exponential Form Exercise.html

7. Conclusion

1.1 complex-numbers-quiz.pdf

1.2 complex-quiz-solutions.pdf

1. Complex Number Quiz.html

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تولید کننده: Udemy-Training