Complex Numbers What if we want to add two sinusoids?

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Presentation transcript:

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

Complex Numbers,Intro (video)

Complex Nums – Rectangular

Complex Nums – Rectangular adding and subtracting (video)

Complex Nums – Rectangular Dividing (video)

Complex Arithmetic (Rectangular) Given: a = 3 + 4j b= -5 + 6j Find a + b a – b a * b a / b

Complex Numbers – Polar (video)

Conversion: Rect to Polar (video)

Conversion: Rect to Polar (video)

Conversion: Polar to Rect (video)

Euler’s Formula (video)

Polar to Rect (and back) Convert a = 2 – 3j and b = -4 + 5j to polar form: Convert c = 2<30o and d = 4<200o To rectangular form

Complex: Add/Multiply in Polar Form (video)

Complex: Divide in Polar (video)

Summary: Mathematic operation of complex numbers http://www.1728.com/compnumb.htm Addition Subtraction Multiplication Division Reciprocal Square root Complex conjugate Euler’s identity

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

Evaluate the following complex numbers: Example 3 Calculator Demo! Evaluate the following complex numbers: a. b. Solution: a. –15.5 + j13.67 b. 8.293 + j2.2

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