1. SE 207: Modeling and Simulation Lesson 3: Review of Complex Analysis
Dr. Samir Al-Amer
Term 072

2. Complex Numbers Complex numbers: number of the form z = x + j y
where x and y are real numbers and
x: real part of z; x = Re {z}
y: imaginary part of z; y = Im {z}

3. Complex Numbers

4. Representing Complex numbers Rectangular representation
Imaginary axis
s1=x + j y
Imaginary Part y x
Real part
real axis
Complex-plane
(s-plane)

5. Representing Complex numbers Polar representation
Imaginary axis
Imaginary Part y ρ θ x
Real part
real axis
Complex-plane
(s-plane)

6. Conversion between Representations Example
Imaginary axis 4 θ 3
real axis

7. Euler Formula 4 θ 3

8. Complex Numbers Addition /Subtraction

9. Complex Numbers Multiplication/Division

10. Operations Examples

11. More Examples

12. Conjugate
Imaginary axis
real axis
Complex-plane
(s-plane)

13. Conjugate

14. Conjugate

15. Conjugate real/imaginary part

16. Operations Polar coordinate Multiplication/Division

17. An example

18. Keywords Conjugate Modulus Real part Imaginary part Polar coordinates
Complex plane
Imaginary axis
Pure imaginary