Linear Circuits and Systems: Sinusoids and Complex Numbers

In the course, sinusoidal steady-state response of first- and second-order circuits is studied. To prepare for this, we need to review sinusoids and complex numbers.



Learning Objectives

After completing this module, you should be able to:

1. Identify and solve for different sinusoid parameters: amplitude, frequency, phase shift, and instantaneous value.

2. Represent complex numbers in different forms.

3. Perform arithmetic operations on complex numbers. 

 

Videos 

Title: M8V1 – Review of Sinusoids

Summary: This video illustrates the anatomy and various parameters of sinusoid signals, including amplitude, frequency, phase, instantaneous value, and lead/lag.

Learning Objectives: After watching this lecture, you will be able to identify and solve for different sinusoid parameters such as amplitude, frequency, phase shift, and instantaneous value.

Slides With Without Annotations: See the slides

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Title: M8V2  Complex Numbers – Representation

Summary:  This video reviews the three different representations of complex numbers: rectangular, polar, and exponential.

Learning Objectives: After watching this lecture, you will be able to represent complex numbers in different forms – rectangular, polar, and exponential.

Slides Without AnnotationsSee the slides 

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Title: M8V3  Complex Numbers – Operations

Summary:  This video reviews performing simple arithmetic operations on complex numbers: addition, subtraction, conjugation, multiplication, and division. For each operation, we discuss which representation form is more convenient to perform that operation.
Learning Objectives: After watching this lecture, you will be able to perform arithmetic operations such as addition, subtraction, conjugation, multiplication, and division on complex numbers.

Transcript: Read the transcript

Slides Without Annotations: See the slides 

Slides With Annotations: See the slides