1. Complex Numbers in Real Life
King Saud University
Physics Department
Phys 301: Mathematical 2
Tahani Almusidi
Group A+B

2. Complex Numbers in Real Life
History
2000 BC
1500 BC
1000 BC
500 BC
500 AC
1000 AC
1500AC
2000 AC
2017
Natural
1,2,3,......
Fraction
0.2 , 0.3 , , ….
Zero & Negative
0, -1, -2, …….. −𝟏

3. Complex Numbers in Real Life
History
1700 AC
1500 AC
1900 AC
2000AC
2000 AC
2017 i
Imaginary −𝟏
Lateral

4. Complex Numbers in Real Life
Example
Drawing the function
Finding its roots
𝒇 𝒙 = 𝒙 𝟐 +𝟏

5. Complex Numbers in Real Life
Drawing the Function
𝒇 𝒙 = 𝒙 𝟐 +𝟏 x
f(x) 2 5 1 -1 -2

6. Complex Numbers in Real Life
Finding the roots
w/ i
wo/ i
Solution
𝒙 𝟐 +𝟏 = 0
No solution
𝒙 𝟐 +𝟏 ≠ 0

7. Complex Numbers in Real Life
Meaning of i
Rotation by 90º i i i -1 1

8. Complex Numbers in Real Life
Meaning of i
Rotation by 90º

9. Complex Numbers in Real Life
Complex Plane

10. Complex Numbers in Real Life
Addition Rules

11. Complex Numbers in Real Life
King Saud University
Physics Department
Phys 301: Mathematical 2
Tahani Almusidi
Group C & D

12. Complex Numbers in Real Life
Multiplication Rules

13. Complex Numbers in Real Life
Multiplication Rules
By following the rules of Algebra (Rectangular)
By finding the distance and angle (Polar)

14. Complex Numbers in Real Life
Multiplication Rules

15. Complex Numbers in Real Life
Examples
𝒙 𝟑 =𝟏
1- Finding the roots for

16. Complex Numbers in Real Life
Examples
𝒙 𝟑 =𝟏
1- Finding the roots for

17. Complex Numbers in Real Life
Examples
𝒙 𝟖 =𝟏
2- Finding the roots for

18. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0
w/ i
wo/ i

19. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (wo/i)

20. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i)
Input
Output

21. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i)

22. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i)

23. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i) 

24. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i)
?!

25. Complex Numbers in Real Life
Drawing the function 𝑿 𝟐 +1=0 (w/i)

26. Complex Numbers in Real Life
Examples:
1- Drawing a shape

27. Complex Numbers in Real Life
Examples:
2- Drawing a path

28. Complex Numbers in Real Life
Examples:
2- Drawing a path
?!

29. Complex Numbers in Real Life
Examples:
2- Drawing a path

30. Complex Numbers in Real Life
Examples:
2- Drawing a path

31. Complex Numbers in Real Life
Examples:
2- Drawing a path

32. Complex Numbers in Real Life
Examples:
2- Drawing a path