1. Complex Numbers What if we want to add two sinusoids?
V(t) = 5cos(377t + 45 ) + 7sin(377t – 60)
Trig Identity:
Not very pleasant!
To deal more effectively with sinusoidal signals we will learn a new tool:
Complex Numbers

2. Complex Numbers,Intro (video)

3. Complex Nums – Rectangular

4. Complex Nums – Rectangular adding and subtracting (video)

5. Complex Nums – Rectangular Dividing (video)

6. Complex Arithmetic (Rectangular)
Given:
a = 3 + 4j
b= j
Find
a + b
a – b
a * b
a / b

7. Complex Numbers – Polar (video)

8. Conversion: Rect to Polar (video)

9. Conversion: Rect to Polar (video)

10. Conversion: Polar to Rect (video)

11. Euler’s Formula (video)

12. Polar to Rect (and back)
Convert a = 2 – 3j and b = j
to polar form:
Convert c = 2<30o and d = 4<200o
To rectangular form

13. Complex: Add/Multiply in Polar Form (video)

14. Complex: Divide in Polar (video)

15. Summary: Mathematic operation of complex numbers
Addition
Subtraction
Multiplication
Division
Reciprocal
Square root
Complex conjugate
Euler’s identity

16. Polar Complex Mult/Div
Given:
c = 8<45
d = 12<250
Find
c * d
c / d
c* (complex conj of c)

17. Evaluate the following complex numbers:
Example 3 Calculator Demo!
Evaluate the following complex numbers: a. b.
Solution: a. – j b j2.2