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Published byMitchell Walker Modified over 5 years ago
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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
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Complex Numbers,Intro (video)
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Complex Nums – Rectangular
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Complex Nums – Rectangular adding and subtracting (video)
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Complex Nums – Rectangular Dividing (video)
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Complex Arithmetic (Rectangular)
Given: a = 3 + 4j b= j Find a + b a – b a * b a / b
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Complex Numbers – Polar (video)
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Conversion: Rect to Polar (video)
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Conversion: Rect to Polar (video)
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Conversion: Polar to Rect (video)
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Euler’s Formula (video)
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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
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Complex: Add/Multiply in Polar Form (video)
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Complex: Divide in Polar (video)
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Summary: Mathematic operation of complex numbers
Addition Subtraction Multiplication Division Reciprocal Square root Complex conjugate Euler’s identity
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Polar Complex Mult/Div
Given: c = 8<45 d = 12<250 Find c * d c / d c* (complex conj of c)
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Evaluate the following complex numbers:
Example 3 Calculator Demo! Evaluate the following complex numbers: a. b. Solution: a. – j b j2.2
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